<SEC-DOCUMENT>0001288847-18-000021.txt : 20180228
<SEC-HEADER>0001288847-18-000021.hdr.sgml : 20180228
<ACCEPTANCE-DATETIME>20180228201109
ACCESSION NUMBER:		0001288847-18-000021
CONFORMED SUBMISSION TYPE:	4
PUBLIC DOCUMENT COUNT:		1
CONFORMED PERIOD OF REPORT:	20180226
FILED AS OF DATE:		20180228
DATE AS OF CHANGE:		20180228

REPORTING-OWNER:	

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

	FILING VALUES:
		FORM TYPE:		4
		SEC ACT:		1934 Act
		SEC FILE NUMBER:	001-36383
		FILM NUMBER:		18654139

	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
<SEQUENCE>1
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<DESCRIPTION>FORM 4
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        <issuerName>Five9, Inc.</issuerName>
        <issuerTradingSymbol>FIVN</issuerTradingSymbol>
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            <rptOwnerName>Passi Gaurav</rptOwnerName>
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            <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>
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            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>EVP, Product Management</officerTitle>
            <otherText></otherText>
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                    <value>7364</value>
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                <transactionPricePerShare>
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            </conversionOrExercisePrice>
            <transactionDate>
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                <transactionPricePerShare>
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                <transactionAcquiredDisposedCode>
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            <expirationDate>
                <value>2023-12-18</value>
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            <underlyingSecurity>
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                </underlyingSecurityTitle>
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            </securityTitle>
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                <value>4.25</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2018-02-26</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
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            <transactionAmounts>
                <transactionShares>
                    <value>2937</value>
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                <transactionPricePerShare>
                    <value>0</value>
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                <transactionAcquiredDisposedCode>
                    <value>A</value>
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            <expirationDate>
                <value>2024-11-05</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
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                <underlyingSecurityShares>
                    <value>2937.0</value>
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                    <value>8813</value>
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                <directOrIndirectOwnership>
                    <value>D</value>
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            <transactionDate>
                <value>2018-02-26</value>
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                <transactionCode>M</transactionCode>
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                <underlyingSecurityShares>
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                <transactionShares>
                    <value>7364</value>
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                <transactionPricePerShare>
                    <value>0</value>
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                <transactionAcquiredDisposedCode>
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                <underlyingSecurityTitle>
                    <value>Common Stock</value>
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                    <value>51412</value>
                </sharesOwnedFollowingTransaction>
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                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
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        <derivativeTransaction>
            <securityTitle>
                <value>Employee Stock Option (right to buy)</value>
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            <conversionOrExercisePrice>
                <value>25.9</value>
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                <value>2018-02-26</value>
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                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
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                <transactionShares>
                    <value>31034</value>
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                <transactionPricePerShare>
                    <value>0</value>
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                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
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            <exerciseDate>
                <footnoteId id="F7"/>
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            <expirationDate>
                <value>2028-02-26</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>31034.0</value>
                </underlyingSecurityShares>
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                <sharesOwnedFollowingTransaction>
                    <value>31034</value>
                </sharesOwnedFollowingTransaction>
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            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
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        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">The price reported in Column 4 is a weighted average price. These shares were sold in multiple transactions at prices ranging from $29.39 to $29.63, inclusive. The reporting person undertakes to provide Five9, Inc., any security holder of Five9, Inc., or the staff of the Securities and Exchange Commission, upon request, full information regarding the number of shares sold at each separate price within the ranges set forth in this footnote.</footnote>
        <footnote id="F2">The price reported in Column 4 is a weighted average price. These shares were sold in multiple transactions at prices ranging from $29.41 to $29.62, inclusive. The reporting person undertakes to provide Five9, Inc., any security holder of Five9, Inc., or the staff of the Securities and Exchange Commission, upon request, full information regarding the number of shares sold at each separate price within the ranges set forth in this footnote.</footnote>
        <footnote id="F3">The option is fully vested.</footnote>
        <footnote id="F4">The option vests in 48 equal monthly installments beginning on the one month anniversary of November 5, 2014.</footnote>
        <footnote id="F5">The option vests in 48 equal monthly installments beginning on the one month anniversary of February 18, 2016.</footnote>
        <footnote id="F6">The option vests in 48 equal monthly installments beginning on the one month anniversary of February 23, 2017.</footnote>
        <footnote id="F7">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>2018-02-28</signatureDate>
    </ownerSignature>
</ownershipDocument>
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