A 5670 only needs about 5 amps. You will be fine.
One of my systems has an OC'd Q9550, 4 GB RAM, a GTX260 - a card that needs about 100 watts more than yours, a Gigabyte EP45-UD3P motherboard, 3 hard drives and an optical, and a Soundblaster card all powered by a Corsair 750TX.
Running 3 instances of Prime95 to load the CPU and 3DMark06 to load the GPU, it pulls 375 watts from the wall as measured by my Kill-a-Watt meter. Figuring 80% PSU efficiency, the system pulls 300 watts from the PSU.