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    <schemaVersion>X0708</schemaVersion>

    <submissionType>D/A</submissionType>

    <testOrLive>LIVE</testOrLive>

    <primaryIssuer>
        <cik>0001832231</cik>
        <entityName>Adams Street Co-Investment Fund V B LP</entityName>
        <issuerAddress>
            <street1>C/O ADAMS STREET PARTNERS, LLC</street1>
            <street2>ONE NORTH WACKER DRIVE, SUITE 2700</street2>
            <city>CHICAGO</city>
            <stateOrCountry>IL</stateOrCountry>
            <stateOrCountryDescription>ILLINOIS</stateOrCountryDescription>
            <zipCode>60606</zipCode>
        </issuerAddress>
        <issuerPhoneNumber>312-553-7890</issuerPhoneNumber>
        <jurisdictionOfInc>DELAWARE</jurisdictionOfInc>
        <issuerPreviousNameList>
            <value>None</value>
        </issuerPreviousNameList>
        <edgarPreviousNameList>
            <value>None</value>
        </edgarPreviousNameList>
        <entityType>Limited Partnership</entityType>
        <yearOfInc>
            <withinFiveYears>true</withinFiveYears>
            <value>2020</value>
        </yearOfInc>
    </primaryIssuer>

    <relatedPersonsList>
        <relatedPersonInfo>
            <relatedPersonName>
                <firstName>N/A</firstName>
                <lastName>ASP Co-Investment Management V LP</lastName>
            </relatedPersonName>
            <relatedPersonAddress>
                <street1>c/o Adams Street Partners, LLC</street1>
                <street2>One North Wacker Drive, Suite 2700</street2>
                <city>Chicago</city>
                <stateOrCountry>IL</stateOrCountry>
                <stateOrCountryDescription>ILLINOIS</stateOrCountryDescription>
                <zipCode>60606</zipCode>
            </relatedPersonAddress>
            <relatedPersonRelationshipList>
                <relationship>Director</relationship>
            </relatedPersonRelationshipList>
            <relationshipClarification>The general partner of the Issuer (the &quot;General Partner&quot;).</relationshipClarification>
        </relatedPersonInfo>
        <relatedPersonInfo>
            <relatedPersonName>
                <firstName>N/A</firstName>
                <lastName>ASP Co-Investment Management V LLC</lastName>
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                <street1>c/o Adams Street Partners, LLC</street1>
                <street2>One North Wacker Drive, Suite 2700</street2>
                <city>Chicago</city>
                <stateOrCountry>IL</stateOrCountry>
                <stateOrCountryDescription>ILLINOIS</stateOrCountryDescription>
                <zipCode>60606</zipCode>
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            <relatedPersonRelationshipList>
                <relationship>Director</relationship>
            </relatedPersonRelationshipList>
            <relationshipClarification>General partner of the General Partner.</relationshipClarification>
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        <relatedPersonInfo>
            <relatedPersonName>
                <firstName>N/A</firstName>
                <lastName>Adams Street Partners, LLC</lastName>
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                <street1>One North Wacker Drive, Suite 2700</street1>
                <city>Chicago</city>
                <stateOrCountry>IL</stateOrCountry>
                <stateOrCountryDescription>ILLINOIS</stateOrCountryDescription>
                <zipCode>60606</zipCode>
            </relatedPersonAddress>
            <relatedPersonRelationshipList>
                <relationship>Director</relationship>
            </relatedPersonRelationshipList>
            <relationshipClarification>Managing Member of the general partner of the General Partner.</relationshipClarification>
        </relatedPersonInfo>
        <relatedPersonInfo>
            <relatedPersonName>
                <firstName>Jeffrey</firstName>
                <middleName>B.</middleName>
                <lastName>Akers</lastName>
            </relatedPersonName>
            <relatedPersonAddress>
                <street1>c/o Adams Street Partners, LLC</street1>
                <street2>One North Wacker Drive, Suite 2700</street2>
                <city>Chicago</city>
                <stateOrCountry>IL</stateOrCountry>
                <stateOrCountryDescription>ILLINOIS</stateOrCountryDescription>
                <zipCode>60606</zipCode>
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            <relatedPersonRelationshipList>
                <relationship>Executive Officer</relationship>
            </relatedPersonRelationshipList>
            <relationshipClarification>Executive Officer of Adams Street Partners, LLC.</relationshipClarification>
        </relatedPersonInfo>
        <relatedPersonInfo>
            <relatedPersonName>
                <firstName>David</firstName>
                <middleName>J.</middleName>
                <lastName>Brett</lastName>
            </relatedPersonName>
            <relatedPersonAddress>
                <street1>c/o Adams Street Partners, LLC</street1>
                <street2>One North Wacker Drive, Suite 2700</street2>
                <city>Chicago</city>
                <stateOrCountry>IL</stateOrCountry>
                <stateOrCountryDescription>ILLINOIS</stateOrCountryDescription>
                <zipCode>60606</zipCode>
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            <relatedPersonRelationshipList>
                <relationship>Executive Officer</relationship>
            </relatedPersonRelationshipList>
            <relationshipClarification>Executive Officer of Adams Street Partners, LLC.</relationshipClarification>
        </relatedPersonInfo>
        <relatedPersonInfo>
            <relatedPersonName>
                <firstName>Sara</firstName>
                <middleName>R.</middleName>
                <lastName>Dasse</lastName>
            </relatedPersonName>
            <relatedPersonAddress>
                <street1>c/o Adams Street Partners, LLC</street1>
                <street2>One North Wacker Drive, Suite 2700</street2>
                <city>Chicago</city>
                <stateOrCountry>IL</stateOrCountry>
                <stateOrCountryDescription>ILLINOIS</stateOrCountryDescription>
                <zipCode>60606</zipCode>
            </relatedPersonAddress>
            <relatedPersonRelationshipList>
                <relationship>Executive Officer</relationship>
            </relatedPersonRelationshipList>
            <relationshipClarification>Executive Officer of Adams Street Partners, LLC.</relationshipClarification>
        </relatedPersonInfo>
        <relatedPersonInfo>
            <relatedPersonName>
                <firstName>Jeffrey</firstName>
                <middleName>T.</middleName>
                <lastName>Diehl</lastName>
            </relatedPersonName>
            <relatedPersonAddress>
                <street1>c/o Adams Street Partners, LLC</street1>
                <street2>One North Wacker Drive, Suite 2700</street2>
                <city>Chicago</city>
                <stateOrCountry>IL</stateOrCountry>
                <stateOrCountryDescription>ILLINOIS</stateOrCountryDescription>
                <zipCode>60606</zipCode>
            </relatedPersonAddress>
            <relatedPersonRelationshipList>
                <relationship>Executive Officer</relationship>
            </relatedPersonRelationshipList>
            <relationshipClarification>Executive Officer of Adams Street Partners, LLC.</relationshipClarification>
        </relatedPersonInfo>
        <relatedPersonInfo>
            <relatedPersonName>
                <firstName>J.</firstName>
                <middleName>Gary</middleName>
                <lastName>Fencik</lastName>
            </relatedPersonName>
            <relatedPersonAddress>
                <street1>c/o Adams Street Partners, LLC</street1>
                <street2>One North Wacker Drive, Suite 2700</street2>
                <city>Chicago</city>
                <stateOrCountry>IL</stateOrCountry>
                <stateOrCountryDescription>ILLINOIS</stateOrCountryDescription>
                <zipCode>60606</zipCode>
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            <relatedPersonRelationshipList>
                <relationship>Executive Officer</relationship>
            </relatedPersonRelationshipList>
            <relationshipClarification>Executive Officer of Adams Street Partners, LLC.</relationshipClarification>
        </relatedPersonInfo>
        <relatedPersonInfo>
            <relatedPersonName>
                <firstName>Miguel</firstName>
                <lastName>Gonzalo</lastName>
            </relatedPersonName>
            <relatedPersonAddress>
                <street1>c/o Adams Street Partners, LLC</street1>
                <street2>One North Wacker Drive, Suite 2700</street2>
                <city>Chicago</city>
                <stateOrCountry>IL</stateOrCountry>
                <stateOrCountryDescription>ILLINOIS</stateOrCountryDescription>
                <zipCode>60606</zipCode>
            </relatedPersonAddress>
            <relatedPersonRelationshipList>
                <relationship>Executive Officer</relationship>
            </relatedPersonRelationshipList>
            <relationshipClarification>Executive Officer of Adams Street Partners, LLC</relationshipClarification>
        </relatedPersonInfo>
        <relatedPersonInfo>
            <relatedPersonName>
                <firstName>Quintin</firstName>
                <lastName>Kevin</lastName>
            </relatedPersonName>
            <relatedPersonAddress>
                <street1>c/o Adams Street Partners, LLC</street1>
                <street2>One North Wacker Drive, Suite 2700</street2>
                <city>Chicago</city>
                <stateOrCountry>IL</stateOrCountry>
                <stateOrCountryDescription>ILLINOIS</stateOrCountryDescription>
                <zipCode>60606</zipCode>
            </relatedPersonAddress>
            <relatedPersonRelationshipList>
                <relationship>Executive Officer</relationship>
            </relatedPersonRelationshipList>
            <relationshipClarification>Executive Officer of Adams Street Partners, LLC.</relationshipClarification>
        </relatedPersonInfo>
        <relatedPersonInfo>
            <relatedPersonName>
                <firstName>Eric</firstName>
                <middleName>R.</middleName>
                <lastName>Mansell</lastName>
            </relatedPersonName>
            <relatedPersonAddress>
                <street1>c/o Adams Street Partners, LLC</street1>
                <street2>One North Wacker Drive, Suite 2700</street2>
                <city>Chicago</city>
                <stateOrCountry>IL</stateOrCountry>
                <stateOrCountryDescription>ILLINOIS</stateOrCountryDescription>
                <zipCode>60606</zipCode>
            </relatedPersonAddress>
            <relatedPersonRelationshipList>
                <relationship>Executive Officer</relationship>
            </relatedPersonRelationshipList>
            <relationshipClarification>Executive Officer of Adams Street Partners, LLC.</relationshipClarification>
        </relatedPersonInfo>
        <relatedPersonInfo>
            <relatedPersonName>
                <firstName>Kelly</firstName>
                <lastName>Meldrum</lastName>
            </relatedPersonName>
            <relatedPersonAddress>
                <street1>c/o Adams Street Partners, LLC</street1>
                <street2>One North Wacker Drive, Suite 2700</street2>
                <city>Chicago</city>
                <stateOrCountry>IL</stateOrCountry>
                <stateOrCountryDescription>ILLINOIS</stateOrCountryDescription>
                <zipCode>60606</zipCode>
            </relatedPersonAddress>
            <relatedPersonRelationshipList>
                <relationship>Executive Officer</relationship>
            </relatedPersonRelationshipList>
            <relationshipClarification>Executive Officer of Adams Street Partners, LLC.</relationshipClarification>
        </relatedPersonInfo>
        <relatedPersonInfo>
            <relatedPersonName>
                <firstName>Robin</firstName>
                <lastName>Murray</lastName>
            </relatedPersonName>
            <relatedPersonAddress>
                <street1>c/o Adams Street Partners, LLC</street1>
                <street2>One North Wacker Drive, Suite 2700</street2>
                <city>Chicago</city>
                <stateOrCountry>IL</stateOrCountry>
                <stateOrCountryDescription>ILLINOIS</stateOrCountryDescription>
                <zipCode>60606</zipCode>
            </relatedPersonAddress>
            <relatedPersonRelationshipList>
                <relationship>Executive Officer</relationship>
            </relatedPersonRelationshipList>
            <relationshipClarification>Executive Officer of Adams Street Partners, LLC.</relationshipClarification>
        </relatedPersonInfo>
        <relatedPersonInfo>
            <relatedPersonName>
                <firstName>Kevin</firstName>
                <lastName>O'Donnell</lastName>
            </relatedPersonName>
            <relatedPersonAddress>
                <street1>c/o Adams Street Partners, LLC</street1>
                <street2>One North Wacker Drive, Suite 2700</street2>
                <city>Chicago</city>
                <stateOrCountry>IL</stateOrCountry>
                <stateOrCountryDescription>ILLINOIS</stateOrCountryDescription>
                <zipCode>60606</zipCode>
            </relatedPersonAddress>
            <relatedPersonRelationshipList>
                <relationship>Executive Officer</relationship>
            </relatedPersonRelationshipList>
            <relationshipClarification>Executive Officer of Adams Street Partners, LLC.</relationshipClarification>
        </relatedPersonInfo>
        <relatedPersonInfo>
            <relatedPersonName>
                <firstName>William</firstName>
                <middleName>B.</middleName>
                <lastName>Sacher</lastName>
            </relatedPersonName>
            <relatedPersonAddress>
                <street1>c/o Adams Street Partners, LLC</street1>
                <street2>One North Wacker Drive, Suite 2700</street2>
                <city>Chicago</city>
                <stateOrCountry>IL</stateOrCountry>
                <stateOrCountryDescription>ILLINOIS</stateOrCountryDescription>
                <zipCode>60606</zipCode>
            </relatedPersonAddress>
            <relatedPersonRelationshipList>
                <relationship>Executive Officer</relationship>
            </relatedPersonRelationshipList>
            <relationshipClarification>Executive Officer of Adams Street Partners, LLC.</relationshipClarification>
        </relatedPersonInfo>
        <relatedPersonInfo>
            <relatedPersonName>
                <firstName>James</firstName>
                <lastName>Walker</lastName>
            </relatedPersonName>
            <relatedPersonAddress>
                <street1>c/o Adams Street Partners, LLC</street1>
                <street2>One North Wacker Drive, Suite 2700</street2>
                <city>Chicago</city>
                <stateOrCountry>IL</stateOrCountry>
                <stateOrCountryDescription>ILLINOIS</stateOrCountryDescription>
                <zipCode>60606</zipCode>
            </relatedPersonAddress>
            <relatedPersonRelationshipList>
                <relationship>Executive Officer</relationship>
            </relatedPersonRelationshipList>
            <relationshipClarification>Executive Officer of Adams Street Partners, LLC.</relationshipClarification>
        </relatedPersonInfo>
    </relatedPersonsList>

    <offeringData>
        <industryGroup>
            <industryGroupType>Pooled Investment Fund</industryGroupType>
            <investmentFundInfo>
                <investmentFundType>Other Investment Fund</investmentFundType>
                <is40Act>false</is40Act>
            </investmentFundInfo>
        </industryGroup>
        <issuerSize>
            <aggregateNetAssetValueRange>Decline to Disclose</aggregateNetAssetValueRange>
        </issuerSize>
        <federalExemptionsExclusions>
            <item>06b</item>
            <item>3C</item>
            <item>3C.7</item>
        </federalExemptionsExclusions>
        <typeOfFiling>
            <newOrAmendment>
                <isAmendment>true</isAmendment>
                <previousAccessionNumber>0001832231-22-000001</previousAccessionNumber>
            </newOrAmendment>
            <dateOfFirstSale>
                <value>2021-04-16</value>
            </dateOfFirstSale>
        </typeOfFiling>
        <durationOfOffering>
            <moreThanOneYear>true</moreThanOneYear>
        </durationOfOffering>
        <typesOfSecuritiesOffered>
            <isOtherType>true</isOtherType>
            <descriptionOfOtherType>Limited Partnership Interests</descriptionOfOtherType>
        </typesOfSecuritiesOffered>
        <businessCombinationTransaction>
            <isBusinessCombinationTransaction>false</isBusinessCombinationTransaction>
            <clarificationOfResponse></clarificationOfResponse>
        </businessCombinationTransaction>
        <minimumInvestmentAccepted>0</minimumInvestmentAccepted>
        <salesCompensationList>
            <recipient>
                <recipientName>Barclays Bank PLC</recipientName>
                <recipientCRDNumber>None</recipientCRDNumber>
                <associatedBDName>None</associatedBDName>
                <associatedBDCRDNumber>None</associatedBDCRDNumber>
                <recipientAddress>
                    <street1>5 The North Colonnade</street1>
                    <city>London</city>
                    <stateOrCountry>X0</stateOrCountry>
                    <stateOrCountryDescription>UNITED KINGDOM</stateOrCountryDescription>
                    <zipCode>E14 4BB</zipCode>
                </recipientAddress>
                <statesOfSolicitationList></statesOfSolicitationList>
                <foreignSolicitation>true</foreignSolicitation>
            </recipient>
            <recipient>
                <recipientName>Greenstone Placement Management FZ-LLC</recipientName>
                <recipientCRDNumber>None</recipientCRDNumber>
                <associatedBDName>None</associatedBDName>
                <associatedBDCRDNumber>None</associatedBDCRDNumber>
                <recipientAddress>
                    <street1>Boulevard Plaza Tower II, 27th Floor</street1>
                    <street2>Downtown Dubai, P.O. Box 73994</street2>
                    <city>Dubai</city>
                    <stateOrCountry>C0</stateOrCountry>
                    <stateOrCountryDescription>UNITED ARAB EMIRATES</stateOrCountryDescription>
                    <zipCode>00000</zipCode>
                </recipientAddress>
                <statesOfSolicitationList></statesOfSolicitationList>
                <foreignSolicitation>true</foreignSolicitation>
            </recipient>
            <recipient>
                <recipientName>Thomas Investment Partners SAS</recipientName>
                <recipientCRDNumber>None</recipientCRDNumber>
                <associatedBDName>None</associatedBDName>
                <associatedBDCRDNumber>None</associatedBDCRDNumber>
                <recipientAddress>
                    <street1>11 rue de Teheran</street1>
                    <city>Paris</city>
                    <stateOrCountry>I0</stateOrCountry>
                    <stateOrCountryDescription>FRANCE</stateOrCountryDescription>
                    <zipCode>75008</zipCode>
                </recipientAddress>
                <statesOfSolicitationList></statesOfSolicitationList>
                <foreignSolicitation>true</foreignSolicitation>
            </recipient>
            <recipient>
                <recipientName>Morgan Stanley Smith Barney LLC</recipientName>
                <recipientCRDNumber>149777</recipientCRDNumber>
                <associatedBDName>None</associatedBDName>
                <associatedBDCRDNumber>None</associatedBDCRDNumber>
                <recipientAddress>
                    <street1>2000 Westchester Avenue</street1>
                    <city>Purchase</city>
                    <stateOrCountry>NY</stateOrCountry>
                    <stateOrCountryDescription>NEW YORK</stateOrCountryDescription>
                    <zipCode>10577</zipCode>
                </recipientAddress>
                <statesOfSolicitationList>
                    <value>All States</value>
                </statesOfSolicitationList>
                <foreignSolicitation>false</foreignSolicitation>
            </recipient>
        </salesCompensationList>
        <offeringSalesAmounts>
            <totalOfferingAmount>Indefinite</totalOfferingAmount>
            <totalAmountSold>399422600</totalAmountSold>
            <totalRemaining>Indefinite</totalRemaining>
            <clarificationOfResponse></clarificationOfResponse>
        </offeringSalesAmounts>
        <investors>
            <hasNonAccreditedInvestors>false</hasNonAccreditedInvestors>
            <totalNumberAlreadyInvested>20</totalNumberAlreadyInvested>
        </investors>
        <salesCommissionsFindersFees>
            <salesCommissions>
                <dollarAmount>0</dollarAmount>
                <isEstimate>true</isEstimate>
            </salesCommissions>
            <findersFees>
                <dollarAmount>0</dollarAmount>
                <isEstimate>true</isEstimate>
            </findersFees>
            <clarificationOfResponse>The entities listed in Item 12 will each receive a fee for certain investors that invest in the Issuer in an amount equal to a percentage of such investors' commitments to the Issuer.</clarificationOfResponse>
        </salesCommissionsFindersFees>
        <useOfProceeds>
            <grossProceedsUsed>
                <dollarAmount>0</dollarAmount>
            </grossProceedsUsed>
            <clarificationOfResponse>Adams Street Partners, LLC will receive a fee for management services. Amount to be paid, number of years to be paid, and extent to be paid out of the adjusted gross proceeds unknown at this time.</clarificationOfResponse>
        </useOfProceeds>
        <signatureBlock>
            <authorizedRepresentative>false</authorizedRepresentative>
            <signature>
                <issuerName>Adams Street Co-Investment Fund V B LP</issuerName>
                <signatureName>/s/ Eric R. Mansell</signatureName>
                <nameOfSigner>Eric R. Mansell</nameOfSigner>
                <signatureTitle>Executive Vice President</signatureTitle>
                <signatureDate>2022-08-22</signatureDate>
            </signature>
        </signatureBlock>
    </offeringData>
</edgarSubmission>
