Have you tried deleting the game data file and restarting GT5 and download all updates?
Once that done, then redownload your purchases from the store.
Game data files tend to get corrupted easily.
Restoring from the back ups will just bring back the corrupt files.
If that don't work then it might be a hard drive problem.
Go here:
http://community.us.playstation.com/message/2252774Follow the instructions and restore file system.
If that didn't help, rebuild the database.
Only those 2 options eh.
Restoring file system/rebuilding database has some side effects just to let you know.
You might lose psn messages and any videos, music you renamed will revert to their original file names. This happens randomly though.
DO NOT RESTORE PS3 SYSTEM lol.
One of those solutions should help. Otherwise it might be a dying hard drive
.