As long as you don't go OCing everything yes. 7970 is a 250W card, and your CPU is a 77W part. You are looking at less then 400W for a system, and you have a 500W gold rated PSU. Don't worry about the PSU, you'll be fine.
You'll want something more if you decide to OC the CPU and the GPU. But as long as you leave everything at stock clocks you'll be fine.