<SEC-DOCUMENT>0001288847-18-000050.txt : 20180402
<SEC-HEADER>0001288847-18-000050.hdr.sgml : 20180402
<ACCEPTANCE-DATETIME>20180402203316
ACCESSION NUMBER:		0001288847-18-000050
CONFORMED SUBMISSION TYPE:	4/A
PUBLIC DOCUMENT COUNT:		1
CONFORMED PERIOD OF REPORT:	20180226
FILED AS OF DATE:		20180402
DATE AS OF CHANGE:		20180402

REPORTING-OWNER:	

	OWNER DATA:	
		COMPANY CONFORMED NAME:			Passi Gaurav
		CENTRAL INDEX KEY:			0001628106

	FILING VALUES:
		FORM TYPE:		4/A
		SEC ACT:		1934 Act
		SEC FILE NUMBER:	001-36383
		FILM NUMBER:		18731058

	MAIL ADDRESS:	
		STREET 1:		C/O FIVE9, INC.
		STREET 2:		4000 EXECUTIVE PARKWAY, SUITE 400
		CITY:			SAN RAMON
		STATE:			CA
		ZIP:			94583

ISSUER:		

	COMPANY DATA:	
		COMPANY CONFORMED NAME:			Five9, Inc.
		CENTRAL INDEX KEY:			0001288847
		STANDARD INDUSTRIAL CLASSIFICATION:	SERVICES-COMPUTER PROCESSING & DATA PREPARATION [7374]
		IRS NUMBER:				943394123
		STATE OF INCORPORATION:			DE
		FISCAL YEAR END:			1231

	BUSINESS ADDRESS:	
		STREET 1:		4000 EXECUTIVE PKWY.
		STREET 2:		SUITE 400
		CITY:			SAN RAMON
		STATE:			CA
		ZIP:			94583
		BUSINESS PHONE:		9252012000

	MAIL ADDRESS:	
		STREET 1:		4000 EXECUTIVE PKWY.
		STREET 2:		SUITE 400
		CITY:			SAN RAMON
		STATE:			CA
		ZIP:			94583

	FORMER COMPANY:	
		FORMER CONFORMED NAME:	Five 9 Inc
		DATE OF NAME CHANGE:	20040428
</SEC-HEADER>
<DOCUMENT>
<TYPE>4/A
<SEQUENCE>1
<FILENAME>wf-form4a_152271558312331.xml
<DESCRIPTION>FORM 4/A
<TEXT>
<XML>
<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0306</schemaVersion>

    <documentType>4/A</documentType>

    <periodOfReport>2018-02-26</periodOfReport>

    <dateOfOriginalSubmission>2018-02-28</dateOfOriginalSubmission>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001288847</issuerCik>
        <issuerName>Five9, Inc.</issuerName>
        <issuerTradingSymbol>FIVN</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001628106</rptOwnerCik>
            <rptOwnerName>Passi Gaurav</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O FIVE9, INC., BISHOP RANCH 8,</rptOwnerStreet1>
            <rptOwnerStreet2>4000 EXECUTIVE PARKWAY, SUITE 400</rptOwnerStreet2>
            <rptOwnerCity>SAN RAMON</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>94583</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>EVP, Product Management</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable></nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Employee Stock Option (right to buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>29.89</value>
                <footnoteId id="F1"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2018-02-26</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>42860</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <value>2028-02-26</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>42860.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>42860</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">This amendment is being filed to correct the exercise price and number of shares of the employee stock option granted to the Reporting Person on February 26, 2018, which were incorrectly listed in the original report.</footnote>
        <footnote id="F2">The option vests in 48 equal monthly installments beginning on the one month anniversary of February 26, 2018.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ David Hill, attorney-in-fact</signatureName>
        <signatureDate>2018-04-02</signatureDate>
    </ownerSignature>
</ownershipDocument>
</XML>
</TEXT>
</DOCUMENT>
</SEC-DOCUMENT>
