TRANSITION AND SEVERANCE AGREEMENT

Exhibit 10.5

TRANSITION AND SEVERANCE AGREEMENT

THIS TRANSITION AND SEVERANCE AGREEMENT (the “Agreement”) entered into as of this 1st day of May, 2014 by and between Hologic, Inc., a Delaware corporation (the “Company”), and David Harding (the “Executive”).

WHEREAS, the Executive previously served as Senior Vice President and General Manager of Women’s Health and has transitioned to the role of Senior Vice President of Corporate Strategy;

WHEREAS, the Executive and the Company previously entered into a Change of Control Agreement, dated November 13, 2008 (as amended, the “Change of Control Agreement”), and a Severance Agreement, dated September 19, 2013 (the “Severance Agreement”);

WHEREAS, the Executive may have been previously entitled to severance benefits pursuant to the Severance Agreement, the Change of Control Agreement, or other agreements or arrangements with the Company, in which case this agreement shall supersede and replace those agreements; and

NOW, THEREFORE, in consideration of the mutual covenants and agreements herein set forth, the parties hereto, each intending to be legally bound, do hereby agree as follows:

1. Term of Agreement. This Agreement shall commence as of the date hereof (the “Effective Date”) and shall continue in effect until Executive’s employment with the Company terminates (the “Term”).

2. Definitions.

2.1 Accrued Compensation. For purposes of this Agreement, “Accrued Compensation” shall mean an amount which shall include all amounts earned or accrued through the Termination Date (as hereinafter defined) but not paid as of the Termination Date, including (i) Base Salary and (ii) reimbursement for reasonable and necessary business expenses incurred by the Executive on behalf of the Company, subject to preapproval by the Company and pursuant to the Company’s expense reimbursement policy in effect at such time, during the period ending on the Termination Date.

2.2 Base Salary. For purposes of this Agreement, “Base Salary” shall mean the greater of the Executive’s annual base salary (a) at the rate in effect on the Termination Date or (b) at the highest rate in effect at any time during the ninety (90) day period immediately prior to the Termination Date, and shall include all amounts of his or her Base Salary that are deferred at the election of the Executive under the qualified and non-qualified employee benefit plans of the Company or any other agreement or arrangement. For avoidance of doubt, Base Salary shall not include any bonus or portion thereof deferred under the Company’s Bonus Deferral Program.

2.3 Bonus. For purposes of this Agreement, “Bonus” shall mean Executive’s target bonus amount for fiscal year 2014 under the Company’s Short-Term Incentive Plan for fiscal year 2014.

2.4 Cause. The Company may terminate the Executive’s employment during the Term of this Agreement for “Cause”. For purposes of this Agreement, “Cause” means (i) disloyalty, gross negligence, willfulness conduct or breach of fiduciary duty to the Company which results in substantial direct or indirect loss, damage or injury to the Company; (ii) Executive’s material violation of the Company’s Code of Conduct and other Company Codes of Conduct or other policies or procedures that are applicable to the Executive; (iii) the commission, indictment, plea of nolo contendere or conviction of Executive of a felony; (iv) the breach of the Executive’s Non-Competition Agreement (as hereinafter defined), or (v) a violation of federal or states securities law or regulations.

2.5 Disability. For purposes of this Agreement, “Disability” shall mean a physical or mental infirmity which impairs the Executive’s ability to substantially perform his or her duties with the Company for a period of ninety (90) consecutive days, and the Executive has not returned to his or her full time employment prior to the Termination Date.

2.6 Non-Competition Agreement. For purposes of this Agreement, “Non-Competition Agreement” means the agreement between the Executive and Cytyc Corporation and its parent, affiliates, successors and assigns containing restrictive covenants pertaining to confidentiality, non-competition and non-solicitation dated October 14, 2005.

2.7 Pro Rata Bonus. For purposes of this Agreement, “Pro Rata Bonus” shall mean an amount equal to the Bonus multiplied by a fraction the numerator of which is the number of months worked in the 2014 fiscal year prior to June 15, 2014 and the denominator of which is 12. Any partial months shall be rounded to the nearest whole number using normal mathematical convention.

3. Employment and Duties.

3.1 Title. Effective as of April 14, 2014, the Executive assumed responsibilities as Senior Vice President of Corporate Strategy of the Company. Subject to the terms and conditions set forth herein, the Executive shall at all times be an “at will” employee.

3.2 Duties. During the Term the Executive agrees to devote time and efforts to the business and affairs of the Company. The Executive agrees that his duties may include travel, as may be reasonably requested by the Company. During the Term, the Executive shall report directly to the Chief Executive Officer. The Executive further agrees to comply with the Company’s policies and procedures as they may be applicable to him as such policies and procedures may be modified from time to time.

3.3 Compensation. During the Term, (i) the Executive shall be entitled to continue to receive base salary at a rate equal to his current annual base salary of $425,000, payable in accordance with the Company’s regular payroll practices; (ii) the Company shall pay Executive a Pro Rata Bonus on the first payroll period following June 15, 2014 (it being understood that Executive shall not be entitled to any further fiscal year 2014 bonus or other bonus thereafter); (iii)

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the Executive’s outstanding stock option, restricted stock unit, performance stock unit and market stock unit awards will remain outstanding and, if applicable, will continue to vest in accordance with and subject to the terms and conditions set forth in the applicable equity incentive plans and award agreements; and (iv) the Executive shall be entitled to participate in any and all retirement (both qualified and non-qualified), medical, dental, life insurance and other employee benefit plans in which he currently participates, all to the extent the Executive remains eligible under the terms of such plans and subject to the terms and conditions of such plans as may be in effect from time to time.

4. Termination of Employment.

4.1 Termination Benefits. If the Executive’s employment with the Company is terminated, then the Executive shall be entitled to the following compensation and benefits:

a. If the Executive’s employment with the Company is terminated (1) by the Company for Cause or Disability, or (2) by reason of the Executive’s death, the Company shall pay to the Executive the Accrued Compensation only.

b. If the Executive’s employment with the Company is terminated by Company without Cause or by Executive for any reason, then the Executive shall be entitled to the following:

i. The Company shall pay the Executive all Accrued Compensation; and

ii. If the Executive’s employment with the Company is terminated prior to September 15, 2015, then the Company shall continue to pay the Executive his or her Base Salary until September 15, 2015, subject to Section 11, in accordance with its normal payroll practices and subject to applicable tax withholding.

c. The Amounts provided for in Sections 4.1(a) and 4.1(b)(i) shall be paid in a single lump sum cash payment within five (5) business days after the Executive’s Termination Date (or earlier, if required by applicable law).

4.2 Mitigation. The Executive shall not be required to mitigate the amount of any payment provided for in this Agreement by seeking other employment or otherwise and no such payment shall be offset or reduced by the amount of any compensation or benefits provided to the Executive in any subsequent employment.

4.3 Other Severance Benefits. The severance pay and benefits provided for in this Section 4 shall be in lieu of any other severance or termination pay to which the Executive may be entitled under the Severance Agreement, the Change of Control Agreement, and any Company severance or termination plan, program, practice or other agreement or arrangement. The Executive’s entitlement to any other compensation or benefits shall be determined in accordance with the Company’s employee benefit plans and other applicable programs, policies and practices then in effect.

5. Notice of Termination. For purposes of this Agreement, “Notice of Termination” shall mean a written notice from the Company or Executive to the other party of termination of the Executive’s employment which indicate the specific termination provision in this Agreement relied

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upon, if any, the effective date of termination, and which sets forth in reasonable detail the facts and circumstances claimed to provide a basis for termination of the Executive’s employment under the provision so indicated. For purposes of this Agreement, no such purported termination shall be effective without such Notice of Termination. For purposes of this Agreement, “Termination Date” shall mean in the case of the Executive’s death, his date of death, and in all other cases, the date specified in the Notice of Termination.

6. Excise Tax Payments.

a. Notwithstanding anything contained in this Agreement to the contrary, to the extent that the payments and benefits provided under this Agreement and benefits provided to, or for the benefit of, the Executive under any other Company plan or agreement (such payments or benefits are collectively referred to as the “Payments”) would be subject to the excise tax (the “Excise Tax”) imposed under Section 4999 of the Internal Revenue Code of 1986, as amended (the “Code”), the Payments shall be reduced (but not below zero) if and to the extent necessary so that no Payment to be made or benefit to be provided to the Executive shall be subject to the Excise Tax (such reduced amount is hereinafter referred to as the “Limited Payment Amount”). Unless the Executive shall have given prior written notice specifying a different order to the Company to effectuate the Limited Payment Amount, the Company shall reduce or eliminate the Payments, by first reducing or eliminating those payments or benefits which are not payable in cash and then by reducing or eliminating cash payments, in each case in reverse order beginning with payments or benefits which are to be paid the farthest in time from the “Determination” (as hereinafter defined). Any notice given by the Executive pursuant to the preceding sentence shall take precedence over the provisions of any other plan, arrangement or agreement governing the Executive’s rights and entitlements to any benefits or compensation.

b. An initial determination as to whether the Payments shall be reduced to the Limited Payment Amount pursuant to the Plan and the amount of such Limited Payment Amount shall be made by an accounting firm at the Company’s expense selected by the Company which is designated as one of the six largest accounting firms in the United States (the “Accounting Firm”). The Accounting Firm shall provide its determination (the “Determination”), together with detailed supporting calculations and documentation, to the Company and the Executive within five (5) days of the Termination Date, if applicable, or such other time as requested by the Company or by the Executive (provided the Executive reasonably believes that any of the Payments may be subject to the Excise Tax), and if the Accounting Firm determines that no Excise Tax is payable by the Executive with respect to a Payment or Payments, it shall furnish the Executive with an opinion, at the Company’s expense, reasonably acceptable to the Executive that no Excise Tax will be imposed with respect to any such Payment or Payments. Within ten (10) days of the delivery of the Determination to the Executive, the Executive shall have the right to dispute the Determination (the “Dispute”). If there is no Dispute, the Determination shall be binding, final and conclusive upon the Company and the Executive subject to the application of Section 6(c) below.

c. As a result of the uncertainty in the application of Sections 4999 and 280G of the Code, it is possible that the Payments to be made to, or provided for the benefit of, the Executive either have been made or have not been made by the Company which, in either case, will be inconsistent with the limitations provided in Section 6(a) (hereinafter referred to as an “Excess Payment” or “Underpayment”, respectively). If it is established pursuant to a final determination of a court, or an Internal Revenue Service (the “IRS”) proceeding which has been finally and conclusively resolved, that an Excess Payment has been made, such Excess Payment shall be deemed

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for all purposes to be a loan to the Executive made on the date the Executive received the Excess Payment and the Executive shall repay the Excess Payment to the Company, on demand (but not less than thirty (30) days after written notice is received by the Executive), together with interest on the Excess Payment at the “Applicable Federal Rate” (as defined in Section 1274(d) of the Code) from the date of the Executive’s receipt of such Excess Payment until the date of such repayment. In the event that it is determined by (i) the Accounting Firm, the Company (which shall include the position taken by the Company, or together with its consolidated group, on its federal income tax return) or the IRS, (ii) pursuant to a determination by a court, or (iii) upon the resolution to the Executive’s satisfaction of the Dispute, that an underpayment has occurred, the Company shall pay an amount equal to the Underpayment to the Executive within thirty (30) days of such determination or resolution, together with interest on such amount at the Applicable Federal Rate from the date such amount would have been paid to the Executive until the date of payment.

d. Notwithstanding anything contained in this Agreement to the contrary, in the event that, according to the Determination, an Excise Tax will be imposed on any Payment or Payments, the Company shall pay to the applicable government taxing authorities, as Excise Tax withholding, the amount of the Excise Tax that the Company has actually withheld from the Payment or Payments.

7. Successors. This Agreement shall be binding upon and shall inure to the benefit of the Company and its permitted successors and assigns. In the event of a merger, sale of substantially all the assets of the Company, or other sale, divestiture, spin-out or other transfer or disposition by the Company of any assets or business of the Company (a “Disposition”), pursuant to which the Executive becomes employed by the successor to such business or assets and such successor agrees to assume the Company’s obligations under this Agreement, then such successor shall become a permitted successor and assign under this Agreement and the Company shall be relieved of all further obligations under this Agreement. In the event of a Disposition, pursuant to which the Executive is offered employment by the successor to such assets or business with a Base Salary no less than his Base Salary with Company and such successor offers to assume the Company’s obligations under this Agreement, and the Executive does not accept such employment, then this Agreement shall terminate immediately and neither the Company nor any such successor shall have any obligations hereunder. Neither this Agreement nor any right or interest hereunder shall be assignable or transferable by the Executive, his or her beneficiaries or legal representatives, except by will or by the laws of descent and distribution. This Agreement shall inure to the benefit of and be enforceable by the Executive’s personal representative.

8. Arbitration. Any dispute, controversy or claim arising out of or relating to this Agreement, or the breach, termination or invalidity hereof, (collectively, a “Claim”) shall be settled by arbitration pursuant to the rules of the American Arbitration Association. Any such arbitration shall be conducted by one arbitrator, with experience in the matters covered by this Agreement, mutually acceptable to the parties. If the parties are unable to agree on the arbitrator within thirty (30) days of one party giving the other party written notice of intent to arbitrate a Claim, the American Arbitration Association shall appoint an arbitrator with such qualifications to conduct such arbitration. The decision of the arbitrator in any such arbitration shall be conclusive and binding on the parties. Any such arbitration shall be conducted in Boston, Massachusetts, unless the Executive consents to a different location.

9. Notice. For the purposes of this Agreement, notices and all other communications provided for in the Agreement (including the Notice of Termination) shall be in writing and shall be (i)

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delivered by hand, (ii) transmitted by facsimile or electronic mail with receipt confirmed, (iii) delivered by overnight courier service with confirmed receipt or (iv) mailed by first class U.S. mail postage pre-paid and registered or certified, return receipt requested and addressed to the respective addresses last given by each party to the other, provided that all notices to the Company shall be directed to the attention of the Board with a copy to the General Counsel of the Company. All notices and communications shall be deemed to have been received on the date of delivery thereof or on the third business day after the mailing thereof, except that notice of change of address shall be effective only upon receipt.

10. Non-Exclusivity of Rights. Nothing in this Agreement shall prevent or limit the Executive’s continuing or future participation in any benefit, bonus, incentive or other plan or program provided by the Company (except for any severance or termination policies, plans, programs or practices) and for which the Executive may qualify, nor shall anything herein limit or reduce such rights as the Executive may have under any other agreements with the Company (except for the Severance Agreement, the Change of Control Agreement and any employment, severance or termination agreements). Amounts which are vested benefits or which the Executive is otherwise entitled to receive under any plan or program of the Company shall be payable in accordance with such plan or program, except as explicitly modified by this Agreement.

11. 409A Compliance.

11.1 Six Month Delay in Payment. Notwithstanding anything to the contrary in this Agreement, if the Executive is a “specified employee” as defined and applied in section 409A of the Code as of the Executive’s Termination Date, then, to the extent any payment under this Agreement constitutes deferred compensation (after taking into account any applicable exemptions from section 409A of the Code, including those specified in Section 11.2) and to the extent required by section 409A of the Code, no payments due under this Agreement may be made until the earlier of: (i) the first day following the sixth month anniversary of the Executive’s Termination Date and (ii) the Executive’s date of death.

11.2 Application of Exemptions. For purposes of section 409A of the Code, each “payment” (as defined by section 409A of the Code) made under this Agreement shall be considered a “separate payment.” In addition, for purposes of section 409A of the Code, each such payment shall be deemed exempt from section 409A of the Code to the fullest extent possible under the “short-term deferral” exemption of Treasury Regulation § 1.409A-1(b)(4), as well as any other applicable exemptions.

11.3 Interpretation of Agreement. Notwithstanding any other provision herein to the contrary, the Company shall make the payments required hereunder in compliance with the requirements of Section 409A of the Code and any interpretative guidance issued thereunder. The Company may, in its sole and absolute discretion, delay payments hereunder or make such other modifications with respect to the timing of payments as it deems necessary to comply with Section 409A of the Code.

12. Release. The Executive agrees that this Agreement, and any rights contemplated hereunder, is subject to and conditioned upon the execution and delivery by the Executive to the Company of a Settlement and Release Agreement (the “Release Agreement”) in favor of the Company, its affiliates and their respective officers, directors, employees and agents (the “Released Parties”) in respect to the Executive’s employment with the Company in a form suitable to the Company and the

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expiration of any revocation period provided for under the Release Agreement. Furthermore, the Executive agrees that that, with the exception of the Accrued Compensation due to him in accordance with the terms hereunder, the payment of any termination benefits under Section 4 is subject to and conditioned upon the execution and delivery by the Executive to the Company of an additional Settlement and Release Agreement (the “Subsequent Release Agreement”) in favor of the Released Parties in respect to the Executive’s employment with the Company and the termination thereof in a form suitable to the Company and the expiration of any revocation period provided for under the Subsequent Release Agreement. Notwithstanding anything herein to the contrary, in the event that the consideration and revocation period provided for in the Subsequent Release Agreement begins in one calendar year and could expire in the second calendar year, then the payment, or commencement of payment, if applicable, provided in Section 4(b)(ii) shall be made or, if applicable, commence in the second calendar year.

13. No Employment Right. This Agreement does not constitute, and shall not be construed to provide, any assurance of continuing employment. Executive’s employment with the Company and of its Successors or Assigns is “at will” and, subject to the terms and conditions of this Agreement, may be terminated by Executive or the Company at any time.

14. Other Change of Control Agreements. The Change of Control Agreement is void ab initio and null and void as of the Effective Date.

15. Miscellaneous. No provision of this Agreement may be modified, waived or discharged unless such waiver, modification or discharge is agreed to in writing, specifying such modification, waiver or discharge, and signed by the Executive and the Company. No waiver by either party hereto at any time of any breach by the other party hereto of, or compliance with, any condition or provision of this Agreement to be performed by such other party shall be deemed a waiver of similar or dissimilar provisions or conditions at the same or at any prior or subsequent time.

16. Governing Law. This Agreement shall be governed by and construed and enforced in accordance with the laws of the Commonwealth of Massachusetts without giving effect to the conflict of laws principles thereof. Any action brought by any party to this Agreement to enforce any decision of an arbitrator made as contemplated in Section 8 above shall be brought and maintained in a court of competent jurisdiction in the Commonwealth of Massachusetts.

17. Severability. The provisions of this Agreement shall be deemed severable, and the invalidity or unenforceability of any provision shall not affect the validity or enforceability of the other provisions hereof.

18. Entire Agreement. This Agreement constitutes the entire agreement between the parties hereto and supersedes all prior severance and employment related agreements, including, without limitation, the Change of Control Agreement and the Severance Agreement, understandings and arrangements, oral or written, between the parties hereto with respect to the subject matter hereof, provided, however, that any option or other equity award agreements, and Non-Competition Agreement shall remain in full force and effect.

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IN WITNESS WHEREOF, the Company has caused this Agreement to be executed by its duly authorized officer and the Executive has executed this Agreement as of the day and year first above written.

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