Exhibit 5.1

Silicon Valley Office • 1755 Embarcadero Road • Palo Alto, California 94303

TELEPHONE: +1.650.739.3939 • FACSIMILE: +1.650.739.3900

November 19, 2020

Five9, Inc.

Bishop Ranch 8

4000 Executive Parkway, Suite 400

San Ramon, California 94583

Re:    Registration Statement on Form S-8 filed by Five9, Inc.

Ladies and Gentlemen:

We have acted as counsel to Five9, Inc., a Delaware corporation (the “Company”), in connection with the registration of 62,594 shares (the “Shares”) of the Company’s common stock, par value $0.001 per share, which may be issued or delivered and sold pursuant to the Inference Technologies Group Inc. 2018 Equity Incentive Plan (the “Plan”), assumed by the Company pursuant to the Agreement and Plan of Merger by and among the Company, Inference Technologies Group Inc., Five9 Acquisition, Inc., and Shareholder Representative Services LLC, as representative, dated October 22, 2020. In connection with the opinion expressed herein, we have examined such documents, records and matters of law as we have deemed relevant or necessary for purposes of such opinion.

Based on the foregoing, and subject to the further limitations, qualifications and assumptions set forth herein, we are of the opinion that the Shares that may be issued or delivered and sold pursuant to the Plan and the authorized forms of award agreements thereunder (the “Award Agreements”) will be, when issued or delivered and sold in accordance with the Plan and the Award Agreements, validly issued, fully paid and nonassessable, provided that the consideration for the Shares is at least equal to the stated par value thereof.

The opinion expressed herein is limited to the General Corporation Law of the State of Delaware, as currently in effect, and we express no opinion as to the effect of the laws of any other jurisdiction on the opinion expressed herein. In addition, we have assumed that the resolutions authorizing the Company to issue or deliver and sell the Shares pursuant to the Plan and the Award Agreements will be in full force and effect at all times at which the Shares are issued or delivered or sold by the Company, and that the Company will take no action inconsistent with such resolutions.

We hereby consent to the filing of this opinion as Exhibit 5.1 to the Registration Statement on Form S-8 filed by the Company to effect registration of the Shares under the Securities Act of 1933 (the “Act”). In giving such consent, we do not thereby admit that we are included in the

AMSTERDAM ATLANTA BEIJING BOSTON BRISBANE BRUSSELS CHICAGO CLEVELAND COLUMBUS DALLAS DETROIT

DUBAI DÜSSELDORF FRANKFURT HONG KONG HOUSTON IRVINE LONDON LOS ANGELES MADRID MELBOURNE

MEXICO CITY MIAMI MILAN MINNEAPOLIS MOSCOW MUNICH NEW YORK PARIS PERTH PITTSBURGH SAN DIEGO

SAN FRANCISCO SÃO PAULO SAUDI ARABIA SHANGHAI SILICON VALLEY SINGAPORE SYDNEY TAIPEI TOKYO WASHINGTON

November 19, 2020

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category of persons whose consent is required under Section 7 of the Act or the rules and regulations of the Securities and Exchange Commission promulgated thereunder.

Very truly yours,

/s/ Jones Day

Jones Day