What resolution are you playing at? Your 4870 should be able to handle 1920x1080 fairly well, if you are at that or below a CPU upgrade would definitely help out more than a GPU upgrade.
Save your money on a GPU upgrade (the 4870 is fine for just about everything out there) and spend $100 or so and upgrade to a Phenom or Athlon x4 CPU, if your MB will support it. Going with the 5870 would be overkill given the processor you currently have.