Without going into the technical side of things (and spending thousands of words boring you with the details), let's just say that numerous experts agree that it's difficult to emulate PS3 games, which is why we haven't seen Sony put in the effort unlike what Microsoft has done with the Xbox 360. However, in light of recent announcements, it appears that Sony is beginning to think about investing the time, money, and effort, to try and emulate PS3 games on the PS5.
According to Jeff Grubb, his sources have told him that Sony is working on an emulation solution to make PS3 games run natively on the PS5.
Sony's expanded PlayStation Plus subscription comes in multiple tiers, with PlayStation Plus Premium being the most expensive variant. Premium will reportedly feature a library of classic games from the PS1, PS2, and PS3.
Unfortunately, while subscribers can already download and play the majority of the selected titles on their PS5 by using emulation, Sony clarified that PS3 games are only available through cloud streaming. This is not an ideal solution as not all Premium subscribers have a fast and stable internet connection that can support streaming video games over the internet consistently, nor will Premium be available in all countries.

