GTA V: Cannot start the application. (CE30005-8)

I have a physical copy of the game and it gets stuck installing at 55%. I left it on last night and when I woke up the PS4 was shut off because of power saving, so I assume it finished. I tried to start the application but it gave me an error "Cannot start the application. (CE-30005-8)". I noticed an update file so I tried installing that but it froze at 6%. I uninstalled once and have rebuilt the database twice but it still gets stuck at some random percentage.

The last game I installed was CoD:AW. I was able to install Infamous after failing to install GTA V. Is there something else I can try?

I don't know the answer. But do you mean you did a system restore/factory reset when "rebuilding the database"? I can say that with older systems I have occasionally (read: very very rarely over many years) had discs that seemed to be... just bad. They would hang up on install or during gameplay at a certain point. Could never get past it. The solution was to return and get another copy. It's a long shot - but if your game disc is returnable that may be a place to turn...

Good luck, maybe someone else with more experience troubleshooting the PS4 specifically has more insight