What are your system specs including PSU rating? Even though the 5750 draws less power than some other video cards, if your PSU is severely underpowered, then you might not have enough power for the GPU.
That or you have a faulty GPU. Have you tried installing it into another computer to see if it works?
I'd RMA the card then. Sounds like you have a bad card.
That or your PSU isn't powerful enough for it. I've never heard of the manufacturer of your PSU, but even cheaply made PSUs that state they are rated at 500W perform a lot less adequately than they are reported to operate at. Even though it SAYS it's 500W doesn't mean it is.