Currently the best manufacturer for graphics card is MSI, through their overclocking application AfterBurner. Neverthless you can't probably do a wrong step with anyone else. The best way how to measure a quality, is via provided warranty. In CR is standard three years for graphic cards and that sounds really convincing.
HIS, MSI, Gigabyte, Sapphire, Asus, Evga..
There's an expected line up>>
from a performance point how the old and new cards correspond
HD 6570 (likely will be stronger than HD 5670 but who knows?)
HD 6770 (same chip like 5770, just rename)
HD 6870 (successor of HD 5770)
HD 5850 (the spirit continue in HD 6950, notice the shift +100 from the previous model)
For a quite nice ladder look here. Hawk cooling for MSI or IceQ from HIS is a Bliss. If you need 2xdvi (not dual link, which means just one connector) or Eyefinity go for it (three panels and more). Otherwise you can shop cheaper. Not so much though.
If so, what would be a good manufactured for a ATI Radeon HD5770?
MSI, HIS and then the others.
And what other good ATI cards are there at that price range?
None. ATI doesn't compete itself in this sector. But will be soon.