I went through a progression of cards made possible by a friendly dealer. My take is the 5770 is a fine card, the 5870 is significantly more powerful and noticeable in CS5 and LR3.. but it really shines when rendering. I couldn't help myself and ended up with the 5970 and it has gobs of power.. basically it's two 5870's running a slightly lower clock speed, but on one card. The 5870 is long, the 5970 longer. Make sure either fits your case. I had to rearrange my drive bays and ended up with the 5970 extending slightly into an empty bay. I think.. either will benefit greatly from an aftermarket cooler such as the Artic Cooler. If you run a web search on 5870/5970 'defective fans' you'll find that after a few weeks of use they start rattling something fierce and their temps are often in the 70-80c range at idle, up to 95c under load. With the Artic Cooler I idle at 45c and full load is 55c.. this is in a 40c ambient temp room. And no noise. Really, none.
So.. the 5770 is fine if only doing images, no gaming, and very limited rendering. The 5870 for games and if you render any video, even flash movies will show benefits. And the 5970 for games, rendering video, its just all out fast. Faster than a 7880 workstation card I also tried. This surprised me. I think its being held back by the driver though not sure.
Three monitors pose a problem. If at least one of your monitors has a displayport input then no problem.. because one must be DP. Or you must use an ACTIVE mini-dp to DVI adapter. AFAIK there are no ACTIVE mini-dp to HDMI adapters, but if anyone knows of one please tell me..
There is a single card out there.. I think the 5870.. that takes care of this on card and does away with the displayport requirement.. so you might want to look at it..