Make sure your PSU is up to the task, although if you can run a HD5770, you should be able to run a HD7850 as well. Both have a single PCIe power connector. A quality 400W-430W PSU like an Antec Earthwatts or Corsair Builder would be sufficient.
^What they said. There is ALWAYS a "bottleneck;" that component that is the greatest constraint on your system's performance. Getting a HD7850 will shift it to the CPU. That would be a solid upgrade. Your PSU will have no trouble with it.
Just go with the 7850 and upgrade the other parts as needed. You gotta start somewhere! My wife runs a 640 with a 5770 and I know if she upgrades her gpu to a 7850 the 640 will not bottleneck and if it did it would be minimal. If you were talking a 7970 or above with a 640 then that is a waist of gpu power.
Your CPU is not going to be damaged, if that's what you're worrying. Sure, it will be working hard, but that's what it's supposed to do. The GPU upgrade will let you get the best possible out of your CPU.
even the radeon hd7770 is a worthy upgrade over the 5770. since he is gonna game at 1680*1050 i dont see why he should spend the extra money over the 7850. 7770 is more than sufficient at that resolution. anything higher will definitely be bottlenecked by the cpu and ram. so just get the 7770 ghz edition
The HD7770 is on the same tier as the HD5770. While I would agree that it is a stronger card (perhaps belongs a tier up), it is still not a major change over the HD5770 and I don't think worth the cost. If a GTX560 or GTX560Ti is in that price range, one of those is probably the smallest performance jump I'd want.
I was looking around the internet at different 7850's and I found on LinusTechTips channel there 7850 required two 6pin power connectors for a single card where as most of the websites say it only requires one? How many connectors does a single 2GB model require?