Tell rockstar about it i'm sure they'll help u .Here's their twitter account @rockstarsupport

I've got an old x360 too, the launch day one.. It works fine for me.
Try cleaning up your HDD or maybe delete all GTA V files and reinstall disc 1

Rockstar haven't made any official comment on the issues yet, though an official troubleshooting statement recommends that users delete all GTA V installation data, clear the Xbox 360's cache and start the installation over. It also states: "If you are still experiencing the error, please try installing to a different memory device."
In response to the difficulties, Xbox Support has released the following guidelines, which has reportedly worked for some. It reads a little like witchcraft (we're surprised step 10 isn't spin around three times on the spot or burn some incense...) but if it comes from the top, it's definitely worth a try.

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.

7. Restart.

8. Install disc 2.

9. Play. (Hopefully.)

Good luck to those affected - we'll update if we hear any official word on a resolution or potential patch from Rockstar.

darren155 wrote Rockstar haven't made any official comment on the issues yet, though an official troubleshooting statement recommends that users delete all GTA V installation data, clear the Xbox 360's cache and start the installation over. It also states: "If you are still experiencing the error, please try installing to a different memory device."
In response to the difficulties, Xbox Support has released the following guidelines, which has reportedly worked for some. It reads a little like witchcraft (we're surprised step 10 isn't spin around three times on the spot or burn some incense...) but if it comes from the top, it's definitely worth a try.

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.

7. Restart.

8. Install disc 2.

9. Play. (Hopefully.)

Good luck to those affected - we'll update if we hear any official word on a resolution or potential patch from Rockstar.

Do Not Install disc 2

Or your game will run awful, and graphics will lower badly.