WARRANT TO PURCHASE STOCK

Exhibit 10.5

THIS WARRANT AND THE SHARES ISSUABLE HEREUNDER HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED, OR ANY APPLICABLE STATE SECURITIES LAWS, AND MAY NOT BE SOLD, PLEDGED OR OTHERWISE TRANSFERRED EXCEPT IN ACCORDANCE WITH APPLICABLE LAW.

WARRANT TO PURCHASE STOCK

THIS WARRANT CERTIFIES THAT, for good and valuable consideration, the receipt of which is hereby acknowledged, SQUARE 1 BANK or its assignee (“Holder”) is entitled to purchase the number of fully paid and nonassessable shares of the class of securities (the “Shares”) of the corporation (the “Company”) at the initial exercise price per Share (the “Warrant Price”) all as set forth above and as adjusted pursuant to Article 2 of this warrant, subject to the provisions and upon the terms and conditions set forth in this warrant.

ARTICLE 1

EXERCISE

1.1 Method of Exercise. Holder may exercise this warrant by delivering this warrant and a duly executed Notice of Exercise in substantially the form attached as Appendix 1 to the principal office of the Company. Unless Holder is exercising the conversion right set forth in Section 1.2, Holder shall also deliver to the Company a check for the aggregate Warrant Price for the Shares being purchased.

1.2 Conversion Right. In lieu of exercising this warrant as specified in Section 1.1, Holder may from time to time convert this warrant, in whole or in part, into a number of Shares determined by dividing (a) the aggregate fair market value of the Shares or other securities otherwise issuable upon exercise of this warrant minus the aggregate Warrant Price of such Shares by (b) the fair market value of one Share. The fair market value of the Shares shall be determined pursuant to Section 1.3.

1.3 Fair Market Value. If the Shares are traded regularly in a public market, the fair market value of the Shares shall be the closing price of the Shares (or the closing price of the Company’s stock into which the Shares are convertible) reported for the business day immediately before Holder delivers its Notice of Exercise to the Company. If the Shares are not regularly traded in a public market, the Board of Directors of the Company shall determine fair market value in its reasonable good faith judgment.

1.4 Delivery of Certificate and New Warrant. Promptly after Holder exercises or converts this warrant, the Company shall deliver to Holder certificates for the Shares acquired and, if this warrant has not been fully exercised or converted and has not expired, a new warrant representing the Shares not so acquired.

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1.5 Replacement of Warrants. On receipt of evidence reasonably satisfactory to the Company of the loss, theft, destruction or mutilation of this warrant and, in the case of loss, theft or destruction, on delivery of an indemnity agreement reasonably satisfactory in form and amount to the Company or, in the case of mutilation, on surrender and cancellation of this warrant, the Company at its expense shall execute and deliver, in lieu of this warrant, a new warrant of like tenor.

1.6 Repurchase on Sale, Merger, or Consolidation of the Company.

1.6.1 “Acquisition.” For the purpose of this warrant, “Acquisition” means (a) any sale, exclusive license, or other disposition of all or substantially all of the assets (including intellectual property) of the Company, or (b) any reorganization, consolidation, merger or sale of the voting securities of the Company or any other transaction where the holders of the Company’s securities before the transaction beneficially own less than 50% of the outstanding voting securities of the surviving entity after the transaction; provided, however, that an Acquisition shall not be deemed to occur as a result of a financing transaction in which newly issued securities of the Company are issued to investors.

1.6.2 Assumption of Warrant. If upon the closing of any Acquisition the successor entity assumes the obligations of this warrant, then this warrant shall be exercisable for the same securities, cash, and property as would be payable for the Shares issuable upon exercise of the unexercised portion of this warrant as if such Shares were outstanding on the record date for the Acquisition and subsequent closing. The Warrant Price shall be adjusted accordingly. The Company shall use reasonable efforts to cause the surviving corporation to assume the obligations of this warrant.

1.6.3 Nonassumption. If upon the closing of any Acquisition in which the consideration consists entirely of cash and/or unrestricted securities, the successor entity does not assume the obligations of this warrant and Holder has not otherwise exercised this warrant in full, then this warrant shall be automatically converted pursuant to Section 1.2 and thereafter Holder shall participate in the Acquisition on the same terms as other holders of the same class of securities of the Company. If the consideration is property other than cash and/or unrestricted securities, the successor entity shall assume this warrant or, at the election of the Company, the Company may purchase this warrant for cash upon the closing of the Acquisition for an amount per Share equal to 1.50 times the Warrant Price.

ARTICLE 2

ADJUSTMENTS TO THE SHARES

2.1 Stock Dividends, Splits, Etc. If the Company declares or pays a dividend on its common stock payable in common stock, or other securities, or subdivides the outstanding common stock into a greater amount of common stock, then upon exercise of this warrant, for each Share acquired, Holder shall receive, without cost to Holder, the total number and kind of securities to which Holder would have been entitled had Holder owned the Shares of record as of the date the dividend or subdivision occurred.

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2.2 Reclassification, Exchange or Substitution. Upon any reclassification, exchange, substitution, or other event that results in a change of the number and/or class of the securities issuable upon exercise or conversion of this warrant, Holder shall be entitled to receive, upon exercise or conversion of this warrant, the number and kind of securities and property that Holder would have received for the Shares if this warrant had been exercised immediately before such reclassification, exchange, substitution, or other event. Such an event shall include any automatic conversion of the outstanding or issuable securities of the Company of the same class or series as the Shares to common stock pursuant to the terms of the Company’s Certificate of Incorporation upon the closing of a registered public offering of the Company’s common stock. The Company or its successor shall promptly issue to Holder a new warrant for such new securities or other property. The new warrant shall provide for adjustments which shall be as nearly equivalent as may be practicable to the adjustments provided for in this Article 2 including, without limitation, adjustments to the Warrant Price and to the number of securities or property issuable upon exercise of the new warrant. The provisions of this Section 2.2 shall similarly apply to successive reclassifications, exchanges, substitutions, or other events.

2.3 Adjustments for Combinations, Etc. If the outstanding Shares are combined or consolidated, by reclassification or otherwise, into a lesser number of shares, the Warrant Price shall be proportionately increased. If the outstanding Shares are split or multiplied, by reclassification or otherwise, into a greater number of shares, the Warrant Price shall be proportionately decreased.

2.4 Adjustments for Diluting Issuances. In the event of the issuance (a “Diluting Issuance”) by the Company after the Issue Date of securities at a price per share less than the Warrant Price, then the number of shares of common stock issuable upon conversion of the Shares shall be adjusted in accordance with those applicable provisions of the Company’s Certificate of Incorporation, as amended, that apply to Diluting Issuances (including any exceptions, exclusions or waivers to an adjustment to the conversion price of the class and series of stock for which the warrant is exercisable).

2.5 No Impairment. The Company shall not, by amendment of its Certificate of Incorporation or through a reorganization, transfer of assets, consolidation, merger, dissolution, issue, or sale of securities or any other voluntary action, avoid or seek to avoid the observance or performance of any of the terms to be observed or performed under this warrant by the Company, but shall at all times in good faith assist in carrying out all the provisions of this Article 2 and in taking all such action as may be necessary or appropriate to protect Holder’s rights under this Article against impairment.

2.6 Certificate as to Adjustments. Upon each adjustment of the Warrant Price, the Company at its expense shall promptly compute such adjustment, and furnish Holder with a certificate of its Chief Financial Officer setting forth such adjustment and the facts upon which such adjustment is based. The Company shall, upon written request, furnish Holder a certificate setting forth the Warrant Price in effect upon the date thereof and the series of adjustments leading to such Warrant Price.

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2.7 Fractional Shares. No fractional Shares shall be issuable upon exercise or conversion of the Warrant and the Number of Shares to be issued shall be rounded down to the nearest whole Share. If a fractional share interest arises upon any exercise or conversion of the Warrant, the Company shall eliminate such fractional share interest by paying Holder an amount computed by multiplying the fractional interest by the fair market value of a full Share (as determined in accordance with Section 1.3).

ARTICLE 3

REPRESENTATIONS AND COVENANTS OF THE COMPANY

3.1 Representations and Warranties. The Company hereby represents and warrants to the Holder as follows:

(a) The initial Warrant Price referenced on the first page of this warrant is equal to the price per share paid in the Company’s most recent equity financing.

(b) All Shares which may be issued upon the exercise of the purchase right represented by this warrant, and all securities, if any, issuable upon conversion of the Shares, shall, upon issuance, be duly authorized, validly issued, fully paid and nonassessable, and free of any liens and encumbrances except for restrictions on transfer provided for herein or under applicable federal and state securities laws.

(c) The Company’s capitalization table attached to this warrant is true and complete as of the Issue Date.

3.2 Notice of Certain Events. If the Company proposes at any time (a) to declare any dividend or distribution upon its common stock, whether in cash, property, stock, or other securities and whether or not a regular cash dividend; (b) to effect any reclassification or recapitalization of common stock; or (c) to merge or consolidate with or into any other corporation, or sell, lease, license, or convey all or substantially all of its assets, or to liquidate, dissolve or wind up, then, in connection with each such event, the Company shall give Holder (1) at least 10 days prior written notice of the date on which a record will be taken for such dividend or distribution (and specifying the date on which the holders of common stock will be entitled thereto) or for determining rights to vote, if any, in respect of the matters referred to in (a); and (2) in the case of the matters referred to in (b) and (c) above at least 10 days prior written notice of the date when the same will take place (and specifying the date on which the holders of common stock will be entitled to exchange their common stock for securities or other property deliverable upon the occurrence of such event).

3.3 Information Rights. So long as the Holder holds this warrant, the Company shall deliver to the Holder (a) promptly after mailing, copies of all communiques to the shareholders of the Company, (b) within one hundred eighty (180) days after the end of each fiscal year of the Company, the annual audited financial statements of the Company certified by independent public accountants of recognized standing and (c) within forty-five (45) days after the end of each of the first three quarters of each fiscal year, the Company’s quarterly, unaudited financial statements. Subsequent to the exercise of the warrant, Holder shall have those

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information rights as set forth in Section 4.1 of the Investor Rights Agreement (as hereinafter defined) as applicable to Investors (as defined therein). The Company’s obligations and Holder’s rights contained in this Section 3.3 shall terminate immediately prior to the effective date of the registration statement pertaining to the Company’s first firm commitment underwritten public offering of its Common Stock under the Securities Act.

3.4 Registration Under Securities Act of 1933, as amended. The Company agrees that, solely with respect to Section 2.3 of the Second Amended and Restated Investor Rights Agreement among the Company and other persons dated as of August 2, 2006, as it may be amended from time to time in accordance with its terms (as long as such amendment does not affect Holder in a manner different from other Holders thereunder) (the “Investor Rights Agreement”), the Shares or, if the Shares are convertible into common stock of the Company, such common stock, shall be “Registrable Securities”, and Holder shall be a “Holder”, and Holder hereby agrees to be bound by the applicable terms and obligations set forth therein with respect to Registrable Securities, including without limitation, the indemnification obligations set forth in Section 2.7(b) and the “Market Stand-off” obligations set forth in Section 2.13.

3.5 Holder Representations and Agreements. In connection with the issuance of this warrant and the Shares (the “Securities”), Holder makes the following representations to the Company:

(a) Holder is aware of the Company’s business affairs and financial condition, and has acquired sufficient information about the Company to reach an informed and knowledgeable decision to acquire the Securities. Holder is purchasing the Securities for its own account for investment purposes only, not as a nominee or agent, and not with a view towards, or for resale in connection with, any “distribution” thereof for purposes of the Securities Act of 1933, as amended (the “Securities Act”). Holder has such knowledge and experience in financial business matters and the undersigned is capable of evaluating the merits and risks of the purchase of the Securities and of protecting its interests in connection therewith.

(b) Holder understands that the Securities have not been registered under the Securities Act or any applicable state securities laws in reliance upon specific exemptions therefrom, which exemptions depend upon, among other things, the bona fide nature of the undersigned’s investment intent as expressed herein.

(c) Holder further understands that the Securities must be held indefinitely, and the undersigned must therefore bear the economic risk therewith, unless the Securities are subsequently registered under the Securities Act and applicable state securities laws or unless an exemption from such registration is otherwise available.

(d) Holder is familiar with the provisions of Rule 144, promulgated pursuant to the Securities Act, which, in substance, permits limited public resale of “restricted securities” acquired, directly or indirectly, from the issuer thereof, in a non-public offering subject to the satisfaction of certain conditions.

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(e) The Securities may be resold in certain limited circumstances subject to the provisions of Rule 144, which requires, among other things, the existence of a public market for the Securities, the availability of certain current public information about the Company, the resale occurring not less than the period of time specified in Rule 144 after a party has purchased and paid for the security to be sold, the sales being affected through a “broker’s transaction” or in transactions directly with a “market maker” and the number of securities being sold during any three month period not exceeding specified limitations.

(f) The undersigned further understands that in the event that all of the applicable requirements of Rule 144 are not satisfied, registration under the Securities Act or an available exception from registration will be required.

(g) Holder is an “accredited investor” as defined in Rule 501(a) of Regulation D promulgated under the Securities Act.

ARTICLE 4

MISCELLANEOUS

4.1 Term: Exercise Upon Expiration. This warrant is exercisable in whole or in part, at any time and from time to time on or before the Expiration Date set forth above; provided, however, that if the Company completes its initial public offering within the one-year period immediately prior to the Expiration Date, the Expiration Date shall automatically be extended until 185 days after the effective date of the Company’s initial public offering. If this warrant has not been exercised prior to the Expiration Date, this warrant shall be deemed to have been automatically exercised on the Expiration Date by “cashless” conversion pursuant to Section 1.2.

4.2 Legends. This warrant and the Shares (and the securities issuable, directly or indirectly, upon conversion of the Shares, if any) shall be imprinted with a legend in substantially the following form:

THIS SECURITY HAS NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED, OR APPLICABLE STATE SECURITIES LAWS, AND MAY NOT BE SOLD, PLEDGED OR OTHERWISE TRANSFERRED EXCEPT IN ACCORDANCE WITH APPLICABLE LAW.

4.3 Compliance with Securities Laws on Transfer. This warrant and the Shares issuable upon exercise of this warrant (and the securities issuable, directly or indirectly, upon conversion of the Shares, if any) may not be transferred or assigned in whole or in part without compliance with applicable federal and state securities laws by the transferor and the transferee.

4.4 Transfer Procedure. Subject to the provisions of Section 4.3, Holder may transfer all or part of this warrant or the Shares issuable upon exercise of this warrant (or the securities issuable, directly or indirectly, upon conversion of the Shares, if any) by giving the Company notice of the portion of the warrant being transferred setting forth the name, address and taxpayer identification number of the transferee and surrendering this warrant to the Company for reissuance to the transferee(s) (and Holder, if applicable).

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4.5 Notices. All notices and other communications from the Company to the Holder, or vice versa, shall be deemed delivered and effective when given personally or mailed by first-class registered or certified mail, postage prepaid, at such address as may have been furnished to the Company or the Holder, as the case may be, in writing by the Company or such Holder from time to time. All notices to the Holder shall be addressed as follows:

Square 1 Bank

Attn: Warrant Administrator

406 Blackwell Street, Suite 240

Durham, NC 27701

4.6 Amendments. This warrant and any term hereof may be changed, waived, discharged or terminated only by an instrument in writing signed by the party against which enforcement of such change, waiver, discharge or termination is sought.

4.7 Attorneys’ Fees. In the event of any dispute between the parties concerning the terms and provisions of this warrant, the party prevailing in such dispute shall be entitled to collect from the other party all costs incurred in such dispute, including reasonable attorneys’ fees.

4.8 Governing Law. This warrant shall be governed by and construed in accordance with the laws of the State of Delaware, without giving effect to its principles regarding conflicts of law.

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APPENDIX 1

NOTICE OF EXERCISE

1. The undersigned hereby elects to purchase                              shares of the                              stock of LIPOSCIENCE, INC. pursuant to the terms of the attached warrant, and tenders herewith payment of the purchase price of such shares in full.

2. The undersigned hereby elects to convert the attached warrant into shares in the manner specified in the warrant. This conversion is exercised with respect to                              of the shares covered by the warrant.

[Strike paragraph that does not apply.]

3. Please issue a certificate or certificates representing said shares in the name of the undersigned or in such other name as is specified below:

Square 1 Bank

Attn: Warrant Administrator

406 Blackwell Street, Suite 240

Durham, NC 27701

4. The undersigned represents it is acquiring the shares solely for its own account and not as a nominee for any other party and not with a view toward the resale or distribution thereof except in compliance with applicable securities laws.