Sony Interactive Entertainment (SIE) CEO Jim Ryan has expressly stated that there will be no backwards compatibility (BC) to the PS1, PS2, and PS3 for the upcoming PlayStation 5. However, just as the PS5 BC question appeared to be put to bed, social media commenter HipHopGamer claimed that disc-based full BC was still a thing.
https://www.notebookcheck.net/PlayStation-5-backwards-compatibility-question-creates-unlikely-conflict-SIE-CEO-Jim-Ryan-vs-gaming-personality-HipHopGamer.494606.0.html
I feel it's going to be something simple as PSNow on PS5 with the ability to stream PS1, 2, 3, and 4 games to the console. The PS4 already has PSNow and you can stream PS2, 3, and 4 games to it already. I don't see native BC but I do see games streamed to the console on online servers made to run such games.
It doesn't even have ps4 bc - they had to say they do after ms' revealing extensive work for it and sony started working on it very recently and why first said 100(s) ps4 games will be bc and now saying 99%.
Having said that, just buy a ps4 pro :)