Five Prime Therapeutics (FPRX) 10-Q 2020 Q3 Quarterly report

Exhibit 32.1

CERTIFICATION PURSUANT TO

18 U.S.C. SECTION 1350,

AS ADOPTED PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

In connection with the Quarterly Report on Form 10-Q of Five Prime Therapeutics, Inc. (“Five Prime”) for the quarter ended September 30, 2020, as filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, Thomas Civik, President and Chief Executive Officer of Five Prime, certify, pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that to the best of my knowledge:

(1) The Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934, as amended; and

(2) The information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of Five Prime.

Dated: November 3, 2020

/s/ Thomas Civik

Thomas Civik

President and Chief Executive Officer

(Principal Executive Officer)