Exhibit 10.5 THIS SECOND SUPPLEMENTAL INDENTURE (the “Second Supplemental Indenture”), dated as of June 4, 2026 (the “Effective Date”), is entered into by and between Gossamer Bio, Inc., a Delaware corporation (the “Company”), and Wilmington Trust, National Association, as trustee under the Indenture (the “Trustee”). Capitalized terms used herein and not otherwise defined herein shall have the meanings ascribed thereto in the Indenture (as defined below). RECITALS WHEREAS, the Company and the Trustee are parties to an indenture, dated as of May 21, 2020, as amended and supplemented by a first supplemental indenture (the “First Supplemental Indenture”), dated as of May 21, 2020 (collectively, the “Original Indenture” and, as amended by this Second Supplemental Indenture, the “Indenture”), which Indenture governs the 5.00% Convertible Senior Notes due 2027 issued by the Company (the “2027 Notes”) under and in accordance with the provisions of the Indenture; WHEREAS, Sections 8.02 and 8.06 of the First Supplemental Indenture provide that the Company and the Trustee may enter into a supplemental indenture to the Indenture for the purpose of amending or supplementing the Indenture or the 2027 Notes or waiving compliance with the provisions of the Indenture or the 2027 Notes with the written consent of the Holders of at least a majority of the aggregate principal amount of the 2027 Notes then outstanding; WHEREAS, on May 18, 2026, the Company commenced an exchange offer (the “Exchange Offer”) pursuant to which it offered to exchange any and all outstanding 2027 Notes for new 7.50% Convertible Senior Secured First Lien Notes due 2030 issued by the Company (the “New Notes”), shares of its common stock, par value $0.0001 per share (the “New Shares”), or, in certain scenarios, prefunded warrants (the “Prefunded Warrants” and, together with the New Shares, the “Equity Securities”), and purchase warrants (the “Purchase Warrants” and, together with the New Notes and the Equity Securities, the “Offered Securities”), upon the terms and subject to the conditions set forth in an exchange offer memorandum and consent solicitation statement, dated as of May 18, 2026 (the “Offering Memorandum”); WHEREAS, concurrently with the Exchange Offer, the Company solicited consents from the Holders of the 2027 Notes to certain proposed amendments (the “Proposed Amendments”) to the Original Indenture and the 2027 Notes, as described in the Offering Memorandum and set forth in Section 1.01 of this Second Supplemental Indenture; WHEREAS, the Company has received and caused to be delivered to the Trustee evidence of the consent to the Proposed Amendments received from Holders of a majority of the aggregate principal amount of the outstanding 2027 Notes (the “Requisite Consents”); WHEREAS, the Company and the Trustee desire to enter into this Second Supplemental Indenture on the Effective Date in order to give effect to the Proposed Amendments, which shall become operative immediately following the issuance of the Offered Securities on the settlement date of the Exchange Offer (the “Operative Date”); and WHEREAS, all acts and requirements necessary to make this Second Supplemental Indenture, when executed by the parties hereto, a legal, valid and binding supplement to the Original Indenture, according to its terms and the terms of the Original Indenture, have been done and performed. NOW, THEREFORE, the parties hereto covenant and agree for the benefit of all Holders of the 2027 Notes, as follows: ARTICLE ONE AMENDMENTS 1.01 Certain Amendments to the Indenture and the 2027 Notes. Effective on the Operative Date, the Indenture and the 2027 Notes, as applicable, are hereby amended as follows:
(a) Section 3.02—Exchange Act Reports, Section 3.03—Compliance and Default Certificates, Article 6— Successors (merger covenant), Section 7.01(A)(v)—Events of Default (failure to comply with Article 6), Section 7.01(A)(vii)—Events of Default (cross defaults), and Section 7.01(A)(viii)—Events of Default (judgments) of the First Supplemental Indenture shall be deleted in their entirety and replaced with “RESERVED.” For the avoidance of doubt, on and after the Operative Date, the failure to comply with the terms of any of the foregoing Sections or Article 6 of the First Supplemental Indenture and the corresponding provisions of the 2027 Notes shall no longer constitute a Default or an Event of Default under the Indenture or the 2027 Notes and shall no longer have any consequence under the Indenture or the 2027 Notes. (b) To the extent that any definitions set forth in Section 1.01 of the First Supplemental Indenture or elsewhere are solely used in the Sections deleted pursuant to subsection (a) above or Article 6, such definitions shall no longer apply or have any consequence in the interpretation of the Indenture or the 2027 Notes. (c) All other provisions of the Indenture, including the terms of the 2027 Notes set forth in Exhibit A to the Original Indenture, and all certificates representing all outstanding 2027 Notes, will be deemed to be amended to reflect the amendments set forth above in this Section 1.01, mutatis mutandis. ARTICLE TWO MISCELLANEOUS 2.01 Relation to Original Indenture; Effectiveness; and Operation. (a) Full Force and Effect. This Second Supplemental Indenture supplements the Original Indenture and shall be a part of and subject to all terms thereof. Except as supplemented hereby, all of the terms, provisions and conditions of the Original Indenture and the 2027 Notes issued thereunder shall continue in full force and effect. In the event of a conflict between the terms and conditions of the Original Indenture and the terms and conditions of this Second Supplemental Indenture, the terms and conditions of this Second Supplemental Indenture shall prevail. For the avoidance of doubt, all references to sections of the Original Indenture amended by this Second Supplemental Indenture shall be to such sections as amended by this Second Supplemental Indenture. (b) Effectiveness of Amendments. Upon the execution and delivery of this Second Supplemental Indenture on the Effective Date and the payment of all outstanding fees and expenses of the Trustee (including the attorneys’ fees and expenses of its counsel, Alston & Bird LLP), this Second Supplemental Indenture shall be effective. Notwithstanding the foregoing, the amendments set forth in Section 1.01 above shall not become operative until the Operative Date. The Company shall provide written notice (which may be via email) of the Operative Date to the Trustee; provided, however, that failure to provide such notice will not impact the operativeness of this Second Supplemental Indenture. (c) GOVERNING LAW; WAIVER OF JURY TRIAL. THIS SECOND SUPPLEMENTAL INDENTURE, AND ANY CLAIM, CONTROVERSY OR DISPUTE ARISING UNDER OR RELATED TO THIS SECOND SUPPLEMENTAL INDENTURE, WILL BE GOVERNED BY AND CONSTRUED IN ACCORDANCE WITH THE LAWS OF THE STATE OF NEW YORK. EACH OF THE COMPANY AND THE TRUSTEE IRREVOCABLY WAIVES, TO THE FULLEST EXTENT PERMITTED BY APPLICABLE LAW, ANY AND ALL RIGHT TO TRIAL BY JURY IN ANY LEGAL PROCEEDING ARISING OUT OF OR RELATING TO THIS SECOND SUPPLEMENTAL INDENTURE OR THE TRANSACTIONS CONTEMPLATED BY THIS SECOND SUPPLEMENTAL INDENTURE. (d) Separability Clause. If any provision of this Second Supplemental Indenture is invalid, illegal or unenforceable, then the validity, legality and enforceability of the remaining provisions of this Second Supplemental Indenture will not in any way be affected or impaired thereby. (e) Confirmation of Indenture. Except as amended and supplemented hereby, the Original Indenture is hereby ratified, confirmed and reaffirmed in all respects. The Original Indenture and this Second Supplemental Indenture shall be read, taken and construed as one and the same instrument.
(f) Counterparts. The parties may sign any number of copies of this Second Supplemental Indenture. Each signed copy will be an original, and all of them together represent the same agreement. Delivery of an executed counterpart of this Second Supplemental Indenture by facsimile, electronically in portable document format or in any other format will be effective as delivery of a manually executed counterpart. The Company agrees to assume all risks arising out of its use of digital signatures and electronic methods to submit communications to the Trustee, including the risk of the Trustee acting on unauthorized instructions and the risk of interception and misuse by third parties. (g) Successors. All agreements of the Company in this Second Supplemental Indenture will bind its successors. All agreements of the Trustee in this Second Supplemental Indenture will bind its successors. (h) Headings. The headings of the Articles and Sections of this Second Supplemental Indenture have been inserted for convenience of reference only, are not to be considered a part of this Second Supplemental Indenture and will in no way modify or restrict any of the terms or provisions of this Second Supplemental Indenture. (i) Trustee Makes No Representation. The recitals contained herein are made by the Company and not by the Trustee, and the Trustee assumes no responsibility for the correctness thereof. The Trustee makes no representation as to the validity or sufficiency of this Second Supplemental Indenture. All rights, protections, privileges, indemnities and benefits granted or afforded to the Trustee under the Indenture shall be deemed incorporated herein by this reference and shall be deemed applicable to all actions taken, suffered or omitted by the Trustee. The Trustee is executing this Second Supplemental Indenture pursuant to the Requisite Consents, which consent is deemed a direction to the Trustee to execute and deliver this Second Supplemental Indenture, and in reliance on the Officer’s Certificate and Opinion of Counsel delivered to it concurrently herewith. [Signature Pages Follow]
[Signature Page – Second Supplemental Indenture] IN WITNESS WHEREOF, the parties have caused this Second Supplemental Indenture to be duly executed all as of the date and year first written above. GOSSAMER BIO, INC. By: /s/ Bryan Giraudo Name: Bryan Giraudo Title: Chief Financial Officer and Chief Operating Officer WILMINGTON TRUST, NATIONAL ASSOCIATION, as Trustee. By: /s/ Barry D. Somrock Name: Barry D. Somrock Title: Vice President