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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2021-11-11</periodOfReport>

    <notSubjectToSection16>1</notSubjectToSection16>

    <issuer>
        <issuerCik>0001829328</issuerCik>
        <issuerName>Fintech Acquisition Corp V</issuerName>
        <issuerTradingSymbol>FTCV</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001300345</rptOwnerCik>
            <rptOwnerName>Loeb Daniel S</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>55 HUDSON YARDS</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10001</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001040273</rptOwnerCik>
            <rptOwnerName>Third Point LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>55 HUDSON YARDS</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10001</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Class A common stock, $0.0001 par value</value>
            </securityTitle>
            <transactionDate>
                <value>2021-11-11</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>63778</value>
                    <footnoteId id="F2"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>10.6128</value>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>2936222</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnote</value>
                    <footnoteId id="F1"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Class A common stock, $0.0001 par value</value>
            </securityTitle>
            <transactionDate>
                <value>2021-11-12</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>179557</value>
                    <footnoteId id="F3"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>10.4859</value>
                    <footnoteId id="F3"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>2756665</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnote</value>
                    <footnoteId id="F1"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Class A common stock, $0.0001 par value</value>
            </securityTitle>
            <transactionDate>
                <value>2021-11-15</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>245440</value>
                    <footnoteId id="F4"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>10.4906</value>
                    <footnoteId id="F4"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>2511225</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnote</value>
                    <footnoteId id="F1"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">The securities disclosed in this Form 4 are owned by certain funds (the &quot;Funds&quot;) managed by Third Point LLC (&quot;Third Point&quot;). Daniel S. Loeb is the Chief Executive Officer of Third Point. By reason of the provisions of Rules 13d-3 and 16a-1 under the Securities Exchange Act of 1934, as amended, Third Point and Mr. Loeb may be deemed to be the beneficial owners of the securities beneficially owned by the Funds. The filing of this statement shall not be deemed an admission that either of Third Point or Mr. Loeb are the beneficial owner of the securities reported herein for purposes of Section 16 of the Securities Exchange Act of 1934, as amended, or otherwise. Third Point and Mr. Loeb hereby disclaim beneficial ownership of all such securities, except to the extent of any indirect pecuniary interest therein.</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 $10.525 to approximately $10.69, inclusive. The Reporting Persons undertake to provide to the Issuer, any security holder of the Issuer, 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 2 to this Form 4.</footnote>
        <footnote id="F3">The price reported in Column 4 is a weighted average price. These shares were sold in multiple transactions at prices ranging from $10.40 to approximately $10.725, inclusive. The Reporting Persons undertake to provide to the Issuer, any security holder of the Issuer, 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 3 to this Form 4.</footnote>
        <footnote id="F4">The price reported in Column 4 is a weighted average price. These shares were sold in multiple transactions at prices ranging from $10.43 to approximately $10.63, inclusive. The Reporting Persons undertake to provide to the Issuer, any security holder of the Issuer, 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 4 to this Form 4.</footnote>
    </footnotes>

    <remarks>The Power of Attorney granted by Daniel S. Loeb in favor of William Song and Joshua L. Targoff, dated February 17, 2021, was previously filed with the SEC on March 4, 2021 as Exhibit 24 to the Form 4 filed by Third Point LLC and Daniel S. Loeb with respect to Radius Global Infrastructure Inc. and is incorporated herein by reference.</remarks>

    <ownerSignature>
        <signatureName>DANIEL S. LOEB, /s/ William Song, as Attorney-in-Fact for Daniel S. Loeb</signatureName>
        <signatureDate>2021-11-15</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>THIRD POINT LLC, /s/ William Song, as Attorney-in-Fact for Daniel S. Loeb, Chief Executive Officer of Third Point</signatureName>
        <signatureDate>2021-11-15</signatureDate>
    </ownerSignature>
</ownershipDocument>
