The HD5770 is a little slower than the HD4890 - if DX11 is really important for you go with the HD5770, otherwise with the HD4890. I got the HD4890 myself and I'm really happy with it. :biggrin:
If you can afford a few more bucks you should go with the HD5850 which is about 10% faster than the HD4890 and supports DX11.