Online or campaign?
If it's online, it may be network related... High latency, packet loss and rubber-banding can and will make bad gameplay.
What 500w PSU is it.
6870 needs roughly 19amps (75*3) / 12v = 18.75amps.
...and yeah, the CPU is on the lowly side for two 6870's... I'd say the cards would def. max out that dual core... You can use MSI Afterburner OSD to check the scaling... if the CPU is bottlenecking (which it probably is) you'll see low scaling and high CPU usage (100%).