The G4560 is arguably not enough for GTA5.
On my system if I turn VSYNC OFF I get far too much screen tearing, but if I use VSYNC (60Hz monitor) and drop below 60FPS at all I get a very JUDDERY (quick stuttering) experience.
I have many, many (far too many) games and GTA5 is one of the view that does this.
Update: I did force on Adaptive VSYNC which turns VSYNC OFF if I can't hit 60FPS (so screen tearing but not the bad judder). That helps with the periodic drops below 60FPS. I also dropped a few settings and managed to mostly avoid drops below 60FPS.
*Here's a video you may like (G4560 + GTX750Ti):
https://www.youtube.com/watch?v=BwOxFUcnz2Y
and
GTX750Ti + G4400 in GTA5 (expand to see his comment below video)...