Despite the fact you have a pretty decent gaming system, the fact remains that GTA requires a lot of gaming muscle to run, especially maxed out.
You don't mention the resolution you are playing at, but I guess 1600x1080 by the FPS you're getting. GTA likes CPU power, so you could try increasing the clock speed beyond 3.2Ghz - heat and voltage permitting. Some more GPU power would go amiss either, a 4870 is a nice card, but you'd need to look towards the ATI 58xx or Nvidia GTX 400 series to max it out.
Either that or just turn down the settings a bit
And I have no idea what the guy above is talking about either....!