Plenty. The HD 5770 uses less power than the HD 4850 which uses 110w.
I believe the HD 5770's power consumption is roughly 80w - 90w under typically gaming scenarios. That works out to 6.67a - 7.5a.
Benchmarking tools like FurMark will cause the video card to draw more power than normal gaming because FurMark is designed to stress everything the video card has to offer at the same time. Games do not do that. See the chart below for the HD 5870.
Based on the review, the HD 5870 typically consumes 107w of power when gaming. Some games stress the video card more than others so do not consider 107w to be the absolute max. As you can see FurMark stress test pushes power consumption up to 161w which is almost a 60% increase.