I'm not aware of working jailbreaks for either Xbox Series or PS5. Its possible that's just a matter of time, but they've both been out for quite a while now it seems like the console manufacturers have finally worked out how to secure them.
Older firmware versions of PS5 are in fact jailbroken (google ps5 jailbreak and you’ll find a bunch of info). I’m not aware of any for Xbox Series but I think that’s more due to lack of interest and the fact that you can run homebrew in development mode already.
