<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0508</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2026-02-17</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001275168</issuerCik>
        <issuerName>FIVE STAR BANCORP</issuerName>
        <issuerTradingSymbol>FSBC</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001858208</rptOwnerCik>
            <rptOwnerName>Lee Michael Eugene</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O FIVE STAR BANCORP</rptOwnerStreet1>
            <rptOwnerStreet2>3100 ZINFANDEL DRIVE, SUITE 100</rptOwnerStreet2>
            <rptOwnerCity>RANCHO CORDOVA</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>95670</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>SVP &amp; Chief Regulatory Officer</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <aff10b5One>0</aff10b5One>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2026-02-17</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>1200</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>40.735</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>36472</value>
                    <footnoteId id="F1"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By self as trustee</value>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">Includes 4,332 shares granted pursuant to the Five Star Bancorp 2021 Equity Incentive Plan (including 3,465 shares which have vested and 867 which are scheduled to vest in equal installments over the remainder of a five-year period, provided Mr. Lee remains employed by Five Star Bancorp on the respective vesting dates),  6,000 shares granted pursuant to the Five Star Bancorp 2021 Equity Incentive Plan (including 2,400 shares which have vested and 3,600 which are scheduled to vest in equal installments over the remainder of a five-year period, provided Mr. Lee remains employed by Five Star Bancorp on the respective vesting dates), and 907 shares granted pursuant to the Five Star Bancorp 2021 Equity Incentive Plan which are scheduled to vest in equal installments over a five-year period beginning in 2026, provided Mr. Lee remains employed by Five Star Bancorp on the respective vesting dates.</footnote>
        <footnote id="F2">Shares are held by The Michael E. Lee &amp; Kaylin M. Fadel-Lee Family Revocable Trust, for which Mr. Lee serves as a trustee.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Michael E. Lee, by Heather C. Luck, Attorney-in-Fact</signatureName>
        <signatureDate>2026-02-19</signatureDate>
    </ownerSignature>
</ownershipDocument>
