The PS5 might not allow for PS2 backwards compatibility but players have found a way around this: the Xbox Series X can run them instead. Doing this, however, might not be a great idea since it could break the console and Microsoft might not be too happy about players doing this. It does raise new questions for Sony to answer about the PS5 console though.
Developer Mode comes pre-installed on the new Xbox Series X console. This can install development builds of software that uses the Universal Windows Platform (UWP) which includes emulators. This means it’s possible to achieve PS2 backwards compatibility on the Xbox Series X by installing a PS2 emulator on the console.
Achieving the PS2 backwards compatibility on the Xbox Series X takes a bit of work. Modern Vintage Gamer on Youtube uploaded a video explaining how it all works (https://youtu.be/psTunlgKOMM). There are still some problems at the moment regarding game file size but most games appear to run well.
Considering the Xbox Series X is capable of PS2 backwards compatibility, there are questions about why Sony opted not to do this for the PS5. The new Sony console offers backwards compatibility with only PS4 games and a handful of others from the PS3 and PS2 via PS Now which is now available worldwide.