Had the same issue when I first started playing the game. Then after about 1 week later of playing like this, my ps3 started giving me the error code 80010514, which is a disc reading error. I then did some research on the web and found that it is a very common issue with very large games and especially GTA5. Follow these steps and hopefully it'll take care of the problem.
1. Start by having the system in standby. (Red Light is only one on)
2. Hold the power button down till the system will turn on and turn off.
3. Press and hold the power button again, and hold it: it will beep as it turns on and then it will double beep. When you hear the double beep immediately take your finger off the power button
4. You will be prompted to plug in your controller via USB and then hit the PS button. (Your now in Recovery Mode)
5. Now you'll see a series of options, this is VERY important, as a miss click will result in erasing your PS3 HDD.
6. The option you want to click is RESTORE FILE SYSTEM.
7. Finally, it is going to restart and bring up a screen reading Corrupted System Data. Your PS will now replace this data Then you choose continue and that should be it.