Offer Letter, dated November 16, 2016, by and between the Registrant and Fred T. Fiedorek

Exhibit 10.5

Rhythm Pharmaceuticals, Inc.

500 Boylston Street — 11th Floor

Boston, MA  02116

Main Telephone:   ###-###-####

www.rhythmtx.com

November 16, 2016

Dr. Fred Fiedorek

c/o Rhythm Pharmaceuticals

500 Boylston Street, 11th Floor

Boston, MA 02116

Dear Fred:

On behalf of Rhythm Pharmaceuticals, Inc., formerly known as Rhythm Metabolic, Inc. (the “Company” or “Rhythm”), I am pleased to set forth below the terms of your employment with the Company.

Employment.  You are currently the Chief Medical Officer of the Company but are an employee of Motus Therapeutics, Inc., an affiliate of the Company (“Motus”).  Your employment with Motus will terminate, and your employment with the Company will begin, on November 16, 2016 (the “Start Date”).  During the term of your employment with the Company, you will continue to hold the position and title of Chief Medical Officer, reporting to the Chief Executive Officer.  While your employment is with the Company, you will also hold the title of Chief Medical Officer of Rhythm Holding Company, LLC (the “Parent”) and Motus.  During the term of your employment with the Company, you will be responsible for performing the duties associated with the position above or as the Company may otherwise assign to you. Your primary place of employment will initially be in the Company’s offices located in Boston, Massachusetts; however, you will be expected to travel as may be necessary to fulfill your responsibilities.  In the course of your employment with Company, you will be subject to, and required to comply with, all Company policies and all applicable laws and regulations.

Base Salary.  During your employment, your salary will be $344,400 annualized, subject to all required and elected taxes and other withholdings.  Your salary may be adjusted from time to time in accordance with normal business practice and in the sole discretion of the Company.

Annual Target Cash Incentive.  Following the end of each fiscal year and subject to the approval by the Company’s Board of Directors, you will be eligible to earn a performance and retention bonus, based on your performance and the Company’s performance, each during the applicable fiscal year, and your continued employment in good standing on the date of incentive distribution.  Your target annual incentive opportunity is 35% of your annualized base salary.

Equity Grant.  Any existing grants of equity you have in the Parent or the Company will be treated consistent with the terms of the applicable agreements under which such awards have been granted.  You may be awarded additional equity grants from time to time in accordance with normal business practice and in the sole discretion of the Company’s Board of Directors or the Parent’s Board of Managers, as the case may be. The terms of any future equity grant will be consistent with any plan under which they are granted and the terms of the applicable agreement under which the award(s) are granted.

Benefits.  You may participate in any and all benefit programs that the Company establishes and makes available to its employees from time to time, subject to the terms and conditions of those programs. The Company’s benefits programs are subject to change at any time in the Company’s sole discretion.  You currently are eligible to receive reimbursement from the Company for 80% of the actual amounts of your medical insurance premiums for yourself and your eligible dependents, until such time as the Company establishes a medical insurance plan.

Vacation.  You are eligible for a maximum of 20 paid vacation days per calendar year.  Your accrual and use of vacation time will be pursuant to any vacation or time off policy the Company may establish or modify from time to time.  The Company’s vacation policy is subject to change at any time in the Company’s sole discretion.

Severance.  If the Company terminates your employment without Cause (as defined below) or you resign your employment with the Company for Good Reason (as defined below) (in either event, a “Qualifying Termination”), subject to your execution of a release acceptable to the Company (the “Release”), the expiration of any revocation period provided in the Release and your continued compliance with the terms of the NDA (as defined below), the Company will pay you an amount equal to your then-current base salary rate (or, if greater, your base salary rate prior to any reduction) for a period of six (6) months (the “Regular Severance Amount”).

If there is a Qualifying Termination within the three (3) months immediately preceding or the twelve (12) months immediately following a “Sale of the Company” (as such term is defined in the Operating Agreement of the Parent, as amended and in effect from time to time), subject to your execution of a Release following your Separation from Service (as defined below), the expiration of any revocation period provided in the Release and your continued compliance with the terms of the NDA, in lieu of any Regular Severance Amount, the Company will pay you an amount equal to your then-current base salary rate for a period of twelve (12) months (the “Sale of the Company Severance Amount”) plus an amount equal to 100% of your annual target cash incentive.

Notwithstanding anything express or implied in this letter to the contrary, if your employment with the Company is terminated by the Company or you at any time prior to or after a Sale of the Company and at the time of such termination you are offered employment on the same terms with either Parent or any subsidiary of Parent and neither Parent nor such subsidiary is at that time itself subject to a Sale of the Company, then the termination of your employment with the Company shall not be deemed or treated as a Qualifying Termination for any purposes of this letter.

Any severance amount to which you may be entitled under this letter will be paid in substantially equal installments in accordance with the Company’s ordinary payroll practices, beginning on the first payroll date following the date that is either (i) 60 days after the date of your Separation from Service, or (ii) in

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the case of a Separation from Service that is a Qualifying Termination that occurs within the three (3) months immediately preceding a Sale of the Company, 60 days after the date of such Sale of the Company. To be eligible for either the Regular Severance Amount or the Sale of the Company Severance Amount, as applicable, you must execute and deliver the Release to the Company and allow it to become effective within 30 days of your Separation from Service or, if later, a Sale of the Company giving rise to a Sale of the Company Severance Amount entitlement.

In addition, if following your Separation from Service, you are eligible for and timely elect continued medical insurance coverage pursuant to COBRA, the Company will reimburse you for the applicable premiums for you and your eligible dependents during the period commencing on the date of your Separation from Service and ending on the earlier to occur of (a) the final day of the Severance Period and (b) the date you otherwise become ineligible for continued coverage under COBRA. Notwithstanding the foregoing, if the Company determines that it cannot provide such reimbursement of premiums to you without potentially violating applicable law, the Company shall not be obligated to make any such payments or reimbursements to you.

If the Qualifying Termination occurs within the three (3) months immediately preceding or the twelve (12) months immediately following a Sale of the Company, then each outstanding equity award in the Parent or the Company held by you shall immediately vest and, if applicable, become exercisable with respect to one hundred percent (100%) of the shares of equity of the Parent or the Company subject thereto.  For purposes of clarity, if at the time of any such Qualifying Termination at least one half of all equity awards granted to you by the Parent or the Company and then held by you are then vested, there will be no further acceleration of vesting as a result of the provisions of this paragraph upon any such Qualifying Termination.  The foregoing provisions of this paragraph shall apply notwithstanding anything express or implied to the contrary in any agreement or award between you and the Company or the Parent, or in any plan of the Company or the Parent, that is applicable to such outstanding equity award.

Notwithstanding anything herein to the contrary, in the event that any compensation or benefit that constitutes “nonqualified deferred compensation” within the meaning of Section 409A of the Internal Revenue Code of 1986, as amended (the “Code”), becomes payable upon the occurrence of a Sale of the Company, such compensation or benefit shall not be paid unless such Sale of the Company constitutes a “change in control event” within the meaning of Section 409A of the Code.

If any payment or benefit you would receive under this letter, when combined with any other payment or benefit you receive pursuant to the termination of your employment with the Company (“Payment”) would (i) constitute a “parachute payment” within the meaning of Section 280G of the Code, and (ii) but for this sentence, be subject to the excise tax imposed by Section 4999 of the Code (the “Excise Tax”), then such Payment shall be either (x) the full amount of such Payment or (y) such lesser amount (with your choice of whether to reduce cash payments or stock option compensation or both) as would result in no portion of the Payment being subject to the Excise Tax, whichever of the foregoing amounts, taking into account the applicable federal, state and local employment taxes, income taxes and the Excise Taxes results in your receipt, on an after-tax basis, of the greater amount of the Payment notwithstanding that all or some portion of the Payment may be subject to the Excise Tax.

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Definitions

Separation from Service.  For purposes of this letter, “Separation from Service” means a “separation from service” within the meaning of Section 409A of the Code. Each installment payment provided under this letter shall at all times be considered a separate and distinct payment for purposes of Section 409A of the Code. Notwithstanding anything in this letter to the contrary, to the extent required to avoid a prohibited distribution under Section 409A of the Code, the benefits provided under this letter will not be provided to you until the earlier of (a) the expiration of the six-month period measured from the date of your Separation from Service with the Company or (b) the date of your death. Upon the first business day after expiration of the relevant period, all payments delayed pursuant to the preceding sentence will be paid in a lump sum and any remaining payments due will be paid as otherwise provided herein.

Cause.  “Cause” shall mean the occurrence of any of the following events by the individual: (i) commission of any crime involving the Company, or any crime involving fraud, breach of trust, or physical or emotional harm to any person, moral turpitude or dishonesty; (ii) any unauthorized use or disclosure of the Company’s proprietary information (other than any such use or disclosure that is not intentional and is not material); (iii) any intentional misconduct or gross negligence that has a material adverse effect on the Company’s business or reputation; (iv) any material breach by you of any agreement between you and the Company that is not cured within thirty (30) days after receipt of written notice from the Company describing any such breach; or (v) repeated and willful failure to perform the duties, functions and responsibilities of the individual’s position after a written warning from the Company.

Good Reason.  “Good Reason” shall mean your resignation from all positions you then hold with the Company if: (A) without your written consent (i) there is a material diminution in the nature or scope of your authorities, duties, or authority; (ii) there is a material reduction of your base salary; provided, however, that a material reduction in your base salary pursuant to a salary reduction program affecting all or substantially all of the employees of the Company and that does not adversely affect you to a greater extent than other similarly situated employees shall not constitute Good Reason; or (iii) you are required to relocate your primary work location to a facility or location that would increase your one way commute distance by more than thirty-five (35) miles from your primary work location as of immediately prior to such change, (B) you provide written notice outlining such conditions, acts or omissions to the Company’s Chief Executive Officer, Chief Financial Officer or General Counsel within thirty (30) days immediately following such material change or reduction, (C) such material change or reduction is not remedied by the Company within thirty (30) days following the Company’s receipt of such written notice and (D) your resignation is effective not later than thirty (30) days after the expiration of such thirty (30) day cure period. “Good Reason” shall also mean your resignation on the one year anniversary of a Sale of the Company from all positions you then hold with the Company or its successor if by that date you have not entered into a written letter or agreement with the Company or such successor that provides for your continued employment with the Company or such successor.  For purposes of clarification, any Qualifying Termination that occurs on the first anniversary of a Sale of the Company shall be deemed and treated as occurring within the twelve (12) months immediately following a Sale of the Company for all purposes of this letter.

Invention, Non-Disclosure, Non-Competition and Non-Solicitation Obligations.  At or prior to the Start Date, you will be required to execute and deliver the Company’s standard form of Employee Confidentiality, Assignment of Inventions, Non-Competition and Non-Solicitation Agreement (the “NDA”), a copy of which has been or will be provided to you separately.

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At-Will Employment.  This letter shall not be construed as an agreement, either express or implied, to employ you for any stated term, and shall in no way alter the Company’s policy of employment at-will.  Similarly, nothing in this letter shall be construed as an agreement, either express or implied, to pay you any compensation or grant you any benefit beyond the end of your employment with the Company, except as otherwise explicitly set forth in this letter.  This letter supersedes all prior understandings, whether written or oral, including, without limitation, your current employment agreement, with respect to the subject matter of this letter.

Please indicate your acceptance of this letter agreement by signing a copy of this offer letter below in the space provided for your signature.

Sincerely,

The foregoing correctly sets forth the terms of my at-will employment with the Company.  I am not relying on any representations other than those set forth above.

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