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TableofContents PROSPECTUSSUPPLEMENT TotheProspectusdatedSeptember19, FiledPursuanttoRule 424(b)(2) 2024FileNo.333-282226 Upto$750millionCommonStock FSKKRCapitalCorp.(“we”,“our”,or“us”)hasenteredintoseparateequitydistributionagreements,datedMay9,2025(the“EquityDistributionAgreements”),witheachofTruistSecurities,Inc.,RBCCapitalMarkets,LLC,KKRCapitalMarketsLLC,andSMBCNikkoSecuritiesAmerica,Inc.(each,a“SalesAgent,”andcollectively,the“SalesAgents”),relatingtothesharesofourcommonstock,parvalue$0.001pershare,pursuanttothisprospectussupplementandtheaccompanyingprospectus.TheEquityDistributionAgreementsprovidethatwemayfromtimetotimeofferandsellsharesofourcommonstockhavinganaggregateofferingpriceofupto$750million. Salesofourcommonstock,ifany,underthisprospectussupplementandtheaccompanyingprospectusmaybemadeinnegotiatedtransactionsortransactionsthataredeemedtobe“atthemarket,”asdefinedinRule415undertheSecuritiesActof1933,asamended(the“SecuritiesAct”),includingsalesmadedirectlyontheNewYorkStockExchange(the“NYSE”)oranysimilarsecuritiesexchangeorsalesmadetoorthroughamarketmakerotherthanonasecuritiesexchange,andbyanyothermethodpermittedbylaw,includingbutnotlimitedtoprivatelynegotiatedtransactions,whichmayincludeblocktrades,asweandtheSalesAgentsmayagree,atpricesrelatedtotheprevailingmarketpricesoratnegotiatedprices.See“PlanofDistribution.” Weareanexternallymanaged,non-diversified,closed-endmanagementinvestmentcompanythathaselectedtoberegulatedasabusinessdevelopmentcompanyundertheInvestmentCompanyActof1940,asamended(the“1940Act”).Ourinvestmentobjectivesaretogeneratecurrentincomeand,toalesserextent,long-termcapitalappreciation.OurinvestmentsandactivitiesaremanagedbyFS/KKRAdvisor,LLC(the“Adviser”),aregisteredinvestmentadviserundertheInvestmentAdvisersActof1940,asamended(the“AdvisersAct”),thatisjointlyoperatedbyanaffiliateofFranklinSquareHoldings,L.P.(“FSInvestments”),andbyKKRCreditAdvisors(US)LLC(“KKRCredit”). OurcommonstockistradedontheNYSEunderthesymbol“FSK”.ThelastreportedclosingpriceforourcommonstockontheNYSEonMay7,2025was$19.45pershare.Thenetassetvalue(“NAV”)ofourcommonstockasofMarch31,2025(thelastdatepriortothedateofthisprospectussupplementonwhichwepublishedNAV)was$23.37pershare. UnderthetermsoftheEquityDistributionAgreements,theSalesAgentswillreceiveacommissionfromusofupto1.5%ofthegrosssalespriceofanysharesofcommonstocksoldthroughsuchSalesAgentundertheEquityDistributionAgreements.TheSalesAgentsarenotrequiredtosellanyspecificnumberordollaramountofcommonstockbutwillusetheircommerciallyreasonableeffortsconsistentwiththeirrespectivesalesandtradingpracticestosellthesharesofourcommonstockofferedbythisprospectussupplementandtheaccompanyingprospectus.WemayalsosellsharesofcommonstocktoaSalesAgent,asprincipalforitsownaccount,atapriceagreeduponatthetimeofsale.IfwesellsharestoaSalesAgentasprincipal,wewillenterintoaseparateagreementwithsuchSalesAgent,settingforththetermsofsuchtransaction,andwewilldescribesuchagreementinaseparateprospectussupplement.See“PlanofDistribution”inthisprospectussupplement.Thesalespricepershareofourcommonstockofferedbythisprospectussupplementandtheaccompanyingprospectus,lesscommissionspayableundertheEquityDistributionAgreementsanddiscounts,ifany,willnotbelessthantheNAVpershareofourcommonstockatthetimeofsuchsale.TheAdvisermay,fromtimetotime,initssolediscretion,paysomeorallofthecommissionspayableundertheEquityDistributionAgreementsormakeadditionalsupplementalpaymentstoensurethatthesalespricepershareofourcommonstockinconnectionwithalloftheofferingsmadehereunderwillnotbelessthanourcurrentNAVpershare.AnysuchpaymentsmadebytheAdviserwillnotbesubjecttoreimbursementbyus. Thisprospectussupplement,theaccompanyingprospectus,andanyrelatedfreewritingprospectus,andthedocumentsincorporatedbyreferenceinthisprospectussupplementandtheaccompanyingprospectus,containimportantinformationaboutusthataprospectiveinvestorshouldknowbeforeinvestinginoursecurities.Pleasereadthisprospectussupplement,theaccompanyingprospectus,andanyrelatedfreewritingprospectus,andthedocumentsincorporatedbyreferenceinthisprospectussupplementandtheaccompanyingprospectus,beforeinvestingandkeepthemforfuturereference.Wefileannual,quarterlyandcurrentreports,proxystatementsandotherinformationaboutuswiththeU.S.SecuritiesandExchangeCommission(the“SEC”).Thisinformationisavailablefreeofchargebycontactingusat201RouseBoulevard,Philadelphia,Pennsylvania19112,bycallinguscollectat(215)495-1150orbyvisitingourwebsiteatwww.fskkradvisor.com/fsk.Informationcontainedonourwebsiteisnotincorporatedbyreferenceintothisprospectussupplementortheaccompanyingprospectus,andyoushouldnotconsiderthatinformationtobepartofthisprospectussupplementortheaccompanyingprospectus.Thecontactinformationprovidedabovemaybeusedbyyoutomakeinvestorinquiries.TheSECalsomaintainsawebsiteatwww.sec.govthatcontainssuchinformation. Weinvestinsecuritiesthatareratedbelowinvestmentgradebyratingagenciesorthatwouldberatedbelowinvestmentgradeiftheywererated.Belowinvestmentgradesecurities,whichareoftenreferredtoas“jun