There’s been no official announcement that Diablo 5 is in development. Period.
There was a single tweet from Mike Ybarra saying the wait between Diablo 4 and Diablo 5 won’t be as long as the wait between Diablo 3 and 4, which was 11 years. In that same tweet he emphasized that there was more content on the way for Diablo 4.
So no, Blizzard is not developing Diablo 5. Not at the moment. In a few years maybe, but not now.