The short answer is, no; the PS5 does not offer full backwards compatibility with PS1, PS2, and PS3 titles. These three generations are mostly incompatible with the PS5 for a variety of reasons.

PS2, PS3, and PS4 for a limited time, in celebration of the 30th anniversary of PlayStation on December 3. A PS5 feature update is now available which, once downloaded, prompts users to "celebrate ...

The PS5 supports 8K@60Hz or 4K@120Hz, so you’ll want to choose an HDMI cable that’s designed to support the latest features of the PS5, including 4K resolution at 120Hz and even 8K resolution ...