First you should know that most demanding games will have framerate that goes up and down, depending on what is going on in the game. You are working with some limitations. One, GTA V works best with Nvidia cards. Two, your FX CPU is not that fast, and 8gb is the minimum GTA V requires. Lastly, a 260x is not that fast either.
My suggestion is to start at the lowest settings. Then experiment by raising settings slightly and checking the framerate. Eventually you'll find the best possible settings that don't cause framerate drops. You can also run a non game benchmark, like 3dmark, to see if your score shows your system is operating normally. Just remember, you have what barely qualifies as an entry level gaming system, you can't expect too much from it.
You can also use something like MSI Afterburner to watch CPU and GPU usage while playing GTA V. If you see numbers up near 100% then your components are running as fast as they can. Also, keep settings within reason. You have 2gb vram, so depending on the game, you might want to stick to medium settings and lower if you're gaming at 1080p.