Answer of your question is No. You can not change the PS5 home screen background and wallpaper.
Your next question is why not?
PS5 have dynamic themes and they will change automatically, when you move home screen game options.
Here, background wallpaper will change automatically according to the current highlighted game option.
PS5 Dynamic Themes is a feature and you can not turn it off.
So, a possible reason to not support background and wallpaper manual change option is dynamic theme feature.