Your fightstick will work on the PS5 if it is a PS4 fightstick that is officially licensed by Sony or if you can upgrade its PCB. Of course, your fightstick should also work on the PS5 if it is advertised as compatible with the PS5.
If you still want to use your current fightstick, check its box or look it up online to know if it was officially licensed by Sony. Otherwise, if you are using a fightstick that you made from a DIY kit or if you bought a fightstick from an individual’s website rather than a company, it might come with the Brook Universal Fighting Board (UFB), which is a multiplatform PCB.
If you have the Brook UFB, you can attach the Brook UFB-UP5 to it for PS5 compatibility. Otherwise, the Brook UFB Fusion combines the UFB & UFB-UP5 for your convenience, and a simpler solution would be the Brook P5 Mini. If you are looking for an adapter, check out the Brook Wingman FGC.