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

    <schemaVersion>X0206</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2021-05-24</periodOfReport>

    <noSecuritiesOwned>0</noSecuritiesOwned>

    <issuer>
        <issuerCik>0001847874</issuerCik>
        <issuerName>Fifth Wall Acquisition Corp. III</issuerName>
        <issuerTradingSymbol>FWAC</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001847658</rptOwnerCik>
            <rptOwnerName>Fifth Wall Acquisition Sponsor III, LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>6060 CENTER DRIVE</rptOwnerStreet1>
            <rptOwnerStreet2>10TH FLOOR</rptOwnerStreet2>
            <rptOwnerCity>LOS ANGELES</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>90045</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <derivativeTable>
        <derivativeHolding>
            <securityTitle>
                <value>Class B Ordinary Shares</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F1"/>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F1"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F1"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Class A Ordinary Shares</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>7067500</value>
                    <footnoteId id="F2"/>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                    <footnoteId id="F3"/>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">As described in the Issuer's Registration Statement under the heading &quot;Description of Securities,&quot; the Class B Ordinary Shares will automatically convert into Class A Ordinary Shares of the Issuer at the time of the Issuer's initial business combination and have no expiration date.</footnote>
        <footnote id="F2">The shares of Class B Ordinary Shares owned by the Reporting Person includes up to 937,500 shares that are subject to forfeiture in the event the underwriters of the initial public offering of the issuer's securities do not exercise in full their over-allotment option as described in the issuer's registration statement.</footnote>
        <footnote id="F3">Fifth Wall Acquisition Sponsor III LLC, is the record holder of the shares reported herein. Fifth Wall Acquisition Sponsor III LLC is governed by two managers. Messr. Andriy Mykhaylovskyy and Brendan Wallace have shared voting and investment power over the shares held by Fifth Wall Acquisition Sponsor III LLC, and disclaim beneficial ownership of the shares held by Fifth Wall Acquisition Sponsor III LLC except to the extent of their pecuniary interest therein.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Andriy Mykhaylovskyy, Manager</signatureName>
        <signatureDate>2021-05-24</signatureDate>
    </ownerSignature>
</ownershipDocument>
