No, you can not play ps1, ps2, or ps3 discs on ps5. But you can play ps4 discs which can be found for very cheap.

However, your ps2 should play both ps1 and ps2 games. Late model ps3's are somewhat easy to come by and are relatively affordable. They also play ps1 games.

Early model PS3's (look up the specific model numbers) would play ps1, ps2, and ps3 games. They're more expensive, have less memory, and are more likely to be faulty. The benefit is being able to play all PS games on 2 consoles instead of 3.