Exhibit 5.1

June 20, 2024

Jaime L. Chase

+1 202 728 7096

jchase@cooley.com

Tempest Therapeutics, Inc.

2000 Sierra Point Parkway, Suite 400

Brisbane, California 94005

Ladies and Gentlemen:

We have acted as counsel to Tempest Therapeutics, Inc., a Delaware corporation (the “Company”), in connection with the offering by the Company of shares of its common stock, par value $0.001 per share (“Common Stock”), having an aggregate offering price of up to $205,000,000 (the “Shares”) pursuant to the Registration Statement on Form S-3 (File No. 333-257990) (the “Registration Statement”) filed with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Securities Act”), the prospectus included in the Registration Statement (the “Base Prospectus”) and the prospectus supplement relating to the shares dated June 20, 2024 and filed with the Commission pursuant to Rule 424(b) under the Securities Act (together with the Base Prospectus, the “Prospectus”). The Shares are to be sold by the Company in accordance with the Open Market Sale Agreement^SM, dated June 20, 2024, by and between the Company and Jefferies LLC (the “Agreement”), as described in the Prospectus.

Each share of Common Stock includes a preferred share purchase right (each, a “Right,” collectively, the “Rights”) as set forth in Rights Agreement (the “Rights Plan”), dated as of October 10, 2023, between the Company and Computershare Trust Company, N.A., as rights agent (the “Rights Agent”).

In connection with this opinion, we have examined and relied upon the Registration Statement, the Prospectus, the Company’s certificate of incorporation and bylaws, each as currently in effect, The Rights Plan, the Agreement and such other records, documents, opinions, certificates, memoranda and instruments as in our judgment are necessary or appropriate to enable us to render the opinion expressed below.

In rendering this opinion, we have assumed the genuineness of all signatures; the authenticity of all documents submitted to us as originals; the conformity to originals of all documents submitted to us as copies; the accuracy, completeness and authenticity of certificates of public officials; and the due authorization, execution and delivery of all documents by all persons other than the Company where authorization, execution and delivery are prerequisites to the effectiveness of such documents. As to certain factual matters, we have relied upon a certificate of an officer of the Company and have not independently verified such matters.

Cooley LLP 1299 Pennsylvania Avenue NW Suite 700 Washington, DC 20004-2400

t: +1 202 842 7800 f: +1 202 842 7899 cooley.com

Tempest Therapeutics, Inc.

June 20, 2024

Page Two

We have assumed (i) that each sale of Shares will be duly authorized by the Board of Directors of the Company, a duly authorized committee thereof or a person or body pursuant to an authorization granted in accordance with Section 152 of the General Corporation Law of the State of Delaware (the “DGCL”) and (ii) that no more than 71,500,000 Shares will be sold pursuant to the Agreement for a consideration not less than the par value of the Common Stock. We express no opinion to the extent that future issuances of securities of the Company, anti-dilution adjustments to outstanding securities of the Company or other matters cause the number of shares of Common Stock issuable under the Agreement to exceed the number of shares of common stock available for issuance by the Company.

With respect to our opinion concerning the Rights:

(i) Our opinion does not address the determination a court of competent jurisdiction may make regarding whether the Company’s board of directors (the “Board”) may be required to redeem or terminate, or take other action with respect to, the Rights or Rights Plan in the future based on the facts and circumstances then existing.

(ii) Our opinion assumes that the Rights Plan has been duly authorized, executed and delivered by the Rights Agent and that members of the Board have acted in a manner consistent with their fiduciary duties as required under applicable law in adopting the Rights Plan. With respect to Rights associated with Shares to be offered in the future under the Registration Statement, our opinion assumes the Rights Plan has not been terminated by the Company or expired by its terms and the Rights have not expired or been redeemed or exchanged by the Company, in each case, prior to the issuance of such Shares.

(iii) Our opinion addresses corporate procedures in connection with the issuance of the Rights associated with the shares of Common Stock of the Company, and not any particular provision of the Rights or the Rights Plan. It should be understood that it is not settled whether the invalidity of any particular provision of a rights agreement or purchase rights issued thereunder would invalidate such rights in their entirety.

Our opinion herein is expressed solely with respect to the DGCL. We express no opinion to the extent that any other laws are applicable to the subject matter hereof and express no opinion and provide no assurance as to compliance with any federal or state securities law, rule or regulation.

On the basis of the foregoing and in reliance thereon, and subject to the qualifications herein stated, we are of the opinion that the Shares and associated Rights, when issued against payment therefor in accordance with the Agreement, the Registration Statement and the Prospectus, will be validly issued, and the Shares will be fully paid and nonassessable.

* * * * *

Our opinion set forth above is limited to the matters expressly set forth in this letter, and no opinion has been or should be implied, or may be inferred, beyond the matters expressly stated. This opinion speaks only as to law and facts in effect or existing as of the date hereof, and we have no obligation or responsibility to update or supplement this opinion to reflect any facts or circumstances that may hereafter come to our attention or any changes in law that may hereafter occur.

Cooley LLP 1299 Pennsylvania Avenue NW Suite 700 Washington, DC 20004-2400

t: +1 202 842 7800 f: +1 202 842 7899 cooley.com

Tempest Therapeutics, Inc.

June 20, 2024

Page Three

We consent to the reference to our firm under the caption “Legal Matters” in the Prospectus and to the filing of this opinion as an exhibit to the Company’s Current Report on Form 8-K to be filed with the Commission for incorporation by reference into the Registration Statement. In giving such consents, we do not thereby admit that we are in the category of persons whose consent is required under Section 7 of the Securities Act of 1933, as amended, or the rules and regulations of the Securities Exchange Commission thereunder.

Sincerely,
Cooley LLP
By:	/s/ Jaime L. Chase
	Jaime L. Chase

Cooley LLP 1299 Pennsylvania Avenue NW Suite 700 Washington, DC 20004-2400

t: +1 202 842 7800 f: +1 202 842 7899 cooley.com