First, please delete all installation data for GTA V if you continue to have issues after this attempt.
After that, put your PS3 into recovery mode:
1.) Turn off PS3 so the red light is on.
2.) Hold and keep holding the power button. The console will turn on, and eventually turn off again.
3.) Once off, with the red light on again, press and hold the power button. You will hear one beep, another single beep after that, and then two beeps in a row. After the two beeps, let go of the power button so it doesn't turn off again and you'll end up in the system recovery menu.
From there, can you please try the "Restore File System" option, and then attempt to reinstall the game again? Let me know if that helps.