Sony Interactive Entertainment President Jim Ryan re-confirms the PS5 won't support or play PS1, PS2, or PS3 games via backward compatibility.

The PS5's backwards compatibility support only extends to the PS4 era, and the next-gen console won't play legacy PS1, PS2, or PS3 games. Sony's Jim Ryan re-iterated the news in a recent interview with Famitsu:
"We have been building devices with a focus on PS5-specific engineering. Among them, PS4 already has 100 million players, so I thought that I would like to play PS4 titles on PS5 as well, so we introduced PS4 compatibility. While achieving that, we focused on incorporating high-speed SSDs and the new DualSense controller in parallel. So, unfortunately, compatibility with them has not been achieved," Ryan said.

The PS5's backwards compatibility is made possible on a logic level instead of a hardware level. The PS4 and the PS5 share a similar x86 architecture which facilitates this kind of interlink. The PS5 is very different from the Cell architecture of the PS3, and those used in the PS2 and PS1.
Previously, Sony integrated chips from the previous generations into the new consoles. So the PS2 featured the entire PS1 chip, and likewise with the PS3. The PS4 didn't have backwards compatibility with the PS3 except for digital and streaming services like PlayStation Now.
This is the third time we've written about legacy games not being supported on the PS5: First in March, following the big PS5 tech talk from Mark Cerny; then in June, a Sony rep denied that older games would be playable on PS5; Finally we have coverage from last month where Ubisoft confirmed games from legacy platforms are unplayable on the next-gen console.
The PlayStation Now subscription will be the only way to play or access these older games on the PS5, and even those games are capped at the PS2 level and don't extend to PS1.
Sony's next-gen PlayStation 5 console will release November 12, 2020 at $399 for the digital-only version, and $499 for the disc-based system.
Check below for side-by-side specs of the entire 9th generation:
