While you cannot play Forza Horizon 5 on PPSSPP, the PSP has a rich library of open-world and arcade racing games that capture a similar spirit. Here are the top 5 alternatives to download (legally, if you dump your own UMDs or find legal backups):

: Forza is an Xbox Game Studios franchise. It has never been ported to any PlayStation hardware, let alone a legacy handheld like the PSP. What "Forza PPSSPP" Files Actually Are

(If you want, I can compare the official system requirements and feature differences between the PC/Xbox release and what to expect on PPSSPP.)