It doesn't seem likely that Bethesda will abandon one of its major IPs entirely, and after the release of both Starfield and The Elder Scrolls 6 a new Fallout game does seem like the natural next step. ... Fallout 5 is not confirmed to be in development.

Is there going to be a Fallout 5?

Fallout 5 will likely arrive in the next few years. Fans are hardly onside with the franchise after their most recent launch, Fallout 76, with plenty of learnings to take from its launch. Fallout 4 wasn't considered the pinnacle of the series either, so there's work to be done making the next one as good as possible.

Is Bethesda working on Fallout 5?

In September 2020, Microsoft bought Bethesda, which means Fallout 5 could one day be an Xbox / PC exclusive, whatever form it takes, whenever it emerges from its underground vault. In the meantime, Bethesda is hard at work on Elder Scrolls 6 and Starfield, so a concrete Fallout 5 release date is likely some ways away.