Exhibit 5.1

Laura A. Berezin

+1 650 843 5128

lberezin@cooley.com

November 13, 2020

Five Prime Therapeutics, Inc.

111 Oyster Point Boulevard

South San Francisco, CA 94080

Ladies and Gentlemen:

You have requested our opinion with respect to certain matters in connection with the offering by Five Prime Therapeutics, Inc., a Delaware corporation (the “Company”), of up to 8,280,000 shares of its common stock, par value $0.001 (the “Shares”), including up to 1,080,000 Shares that may be sold pursuant to the exercise of an option to purchase additional Shares, pursuant to a Registration Statement on Form S-3 (Registration Statement No. 333-228206) (the “Registration Statement”), filed with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Act”), the prospectus included therein (the “Base Prospectus”), and the prospectus supplement, dated November 12, 2020, filed with the Commission pursuant to Rule 424(b) under the Act (together with the Base Prospectus, the “Prospectus”).

In connection with this opinion, we have examined and relied upon the Registration Statement, the Prospectus, the Company’s Amended and Restated Certificate of Incorporation and the Company’s Amended and Restated Bylaws, each as currently in effect, and 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 of all documents by all persons other than the Company where authorization, execution and delivery are prerequisites to the effectiveness thereof. As to certain factual matters, we have relied upon a certificate of an officer of the Company and have not independently verified such matters.

Our opinion herein is expressed solely with respect to the General Corporation Law of the State of Delaware. 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 sold and issued in accordance with the Registration Statement and the Prospectus, will be validly issued, fully paid and nonassessable.

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 a Current Report on Form 8-K to be filed with the Commission for incorporation by reference into the Registration Statement.

COOLEY LLP    3175 HANOVER STREET    PALO ALTO, CA    94304-1130

T: (650) 843-5000 F: (650) 849-7400 COOLEY.COM

Five Prime Therapeutics, Inc.

November 13, 2020

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COOLEY LLP    3175 HANOVER STREET    PALO ALTO, CA    94304-1130

T: (650) 843-5000 F: (650) 849-7400 COOLEY.COM