You might be better off with a GTX 460 because not only are they quite short (i think either the Palit or Zotac one is 9.5") but their power connectors are on the top of the PCB and not the right side. Mostly, the 5850's power connectors are on the right side of the PCB which adds another half an inch to the overall card length.
I got my 5870 and was surprised to see that it did infact fit in the case without having to cut into it. I did need to cut into it to get the power connectors in. but, seeing as how XFX list the 5870 as 11" and the 5850 as 9.5", and you only need an inch for the power connectors, it seems 5850s would have fit fine with no haxing.