I have one of the old Xbox Arcades with a 20GB hard drive and keep having problems with the disc being "unreadable". There's nothing wrong with the disc itself, it's a problem with older consoles. There isn't a proper fix but Xbox Support recommended this;
1. Delete all GTA 5 game data.
2. Clear system cache three times.
3. Delete marketplace data from storage system items.
4. Unplug console for three minutes.
5. Install disc 1.
6. Power off, do not insert disc 2.
8. Install disc 2.
9. Play. (Hopefully.)