Exhibit 5.1

Laura A. Berezin

+1 650 843 5128

lberezin@cooley.com

January 24, 2018

Five Prime Therapeutics, Inc.

Two Corporate Drive

South San Francisco, CA 94080

Ladies and Gentlemen:

You have requested our opinion, as counsel to Five Prime Therapeutics, Inc., a Delaware corporation (the “Company”), with respect to certain matters in connection with the offering by the Company of up to 5,897,435 shares of its common stock, par value $0.001 (the “Shares”), including up to 769,230 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. 333-214411) (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 within the Registration Statement (the “Base Prospectus”), and the prospectus supplement, dated January 24, 2018, and filed with the Commission pursuant to Rule 424(b) of the Rules and Regulations of the Act (the “Prospectus Supplement”). The Base Prospectus and the Prospectus Supplement are collectively referred to as the “Prospectus.” The Shares are to be sold by the Company as described in the Registration Statement and 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, the Company’s Amended and Restated Bylaws and the 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. As to certain factual matters, we have relied upon a certificate of an officer of the Company and have not sought to independently verify 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. This opinion is

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

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

Five Prime Therapeutics, Inc.

January 24, 2018

Page Two

expressed as of the date hereof, and we disclaim any responsibility to advise you of any changes in the facts stated or assumed herein or any changes in applicable law.

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

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