First of all this in no way jeopardizes his PC in any way, lets get that straight. Second of all we know time after time that video card makers ALWAYS over state the PSU requirements. It is a safe bet for the video card maker to weed out the total garbage PSU out there that can only put out half the power they are rated at, the OP's PSU is from a reputable manufacturer and will not fall into the garbage category.
Here is an excert from a tom's hardware review:
"ATI rates the Radeon HD 5770 for 18W of power consumption at idle and 108W maximum board power at load. The Radeon HD 5750 is even lower at 16W idle and 86W under load. The delta there checks out almost exactly, as our Radeon HD 5750 sample used two watts less than our 5770 at idle, and 22W less (instead of the expected 21W) with FurMark running at full tilt."
Now this chart is using a quad core from the same series as the OP (his is dual core). Also this is power drawn from the wall.