Exhibit 5.1

Laura Berezin

+1 650 843 5128

lberezin@cooley.com

August 6, 2020

Five Prime Therapeutics, Inc.

111 Oyster Point Boulevard

South San Francisco, CA 94080

Ladies and Gentlemen:

We have acted as counsel to Five Prime Therapeutics, Inc., a Delaware corporation (the “Company”), in connection with the offering by the Company of up to $75,000,000 of shares (the “Shares”) of the Company’s common stock, par value $0.001 per share (the “Common Stock”), pursuant to a Registration Statement on Form S-3 (File No. 333-228206) (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 dated August 6, 2020, filed with the Commission pursuant to Rule 424(b) of the Rules and Regulations of the Act (together with the Base Prospectus, the “Prospectus”). The Shares are to be sold by the Company in accordance with the Sales Agreement dated August 6, 2020 (the “Agreement”) between the Company and Cowen and Company, LLC, as described in the Prospectus.

In connection with this opinion, we have examined and relied upon (a) the Registration Statement and the Prospectus, (b) the Company’s Amended and Restated Certificate of Incorporation and Amended and Restated Bylaws, each as currently in effect, (c) the Agreement and (d) originals or copies certified to our satisfaction of such records, documents, certificates, memoranda and other instruments as in our judgment are necessary or appropriate to enable us to render the opinion expressed below. 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 by all persons other than the Company of all documents where authorization, execution and delivery are prerequisites to the effectiveness thereof. As to certain factual matters, we have relied upon a certificate of officers of the Company and have not independently verified such matters.

We have assumed (i) that the specific sale of the 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 30,000,000 Shares will be sold. We express no opinion to the extent that future issuances of securities of the Company and/or anti-dilution adjustments to outstanding securities of the Company cause the number of shares of Common Stock outstanding or issuable upon conversion or exercise of outstanding securities of the Company to exceed the number of Shares then issuable under the Agreement.

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, we are of the opinion that the Shares, when issued and paid for in accordance with the Agreement, the Registration Statement and the Prospectus, will be validly issued, fully paid and nonassessable.

Cooley LLP    3175 Hanover Street    Palo Alto, CA    94304-1130

t: (650) 843-5000  f: (650) 849-7400  cooley.com

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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.

Sincerely,

Cooley LLP    3175 Hanover Street    Palo Alto, CA    94304-1130

t: (650) 843-5000  f: (650) 849-7400  cooley.com