All 5000 series cards have DX11.
First you start talking about the 5750 and the 5770, then you start talking about the 5870... getting lost in that part of the sentence. Was the 5870 a typo?
Anyway the 5850 has the best bang for the buck out of all the high end cards vs the 5870 and 5970.
As for 5770 vs 5750 it would be worth the extra money if you have the screen resolution to help back it up.