Here is the debate. The HD5770 is the lesser performing of the (3) cards you listed. With the 4870 being next and 4890 being the best performing. However, the 5770 will draw less power, runs cooler, and is DX11. Remember the 5770 is pretty similar in specs to the 4870 with the exeption of the memory bus, which is 128bit instead of 256bit. This would mean the 48xx card may show better increases during an OC. You have to determine what is more important for you. Do you want a DX11 for for future games that support it, or do you want a faster card NOW for DX10 (or 10.1) games?
Now with your mention of all prices being the same, I would personally go with the 4890 hands down if it were my choice. I had a 4870 and it OCed REALLY REALLY well and saw good improvements. I would assume the 4890 would do even better. I think that running DX11 on a 5770 may put alot of load to the GPU and you would ultimately end up turning down the graphics anyways.
So my suggestion is a 4890. Possibly one with an upgraded cooler. If you plan to xfire, I suggest a cooler that blows the air out the back. TRUST me, this is a bonus when you try to xfire 2 cards. I tried this with (2) 4870's that let the heat in the case and the top card hit 100C and crashed. Blower style coolers have ALOT of benefits.
NOW, here is another question. If you have the extra money and ALOT of patience, I would suggest looking for a 5850 or 5870. When I had issues with my 4870 xfire setup, I caved and ended up selling both on eBay and getting a 5870. BEST choice I made. The card is fantastic. I've heard the 5850 is really impress ive as well. The 5850 will run you $300 and the 5870 $400, as they seemed to have increased the prices a bit. Alot of retailers are completely out of stock and when they get a delivery, they are gone in a matter of 30minutes. I had to babysit Newegg for a few days until I got mine. Just a thought.
But if the 3 cards you listed are your only selection, I say 4890 ALL THE WAY.
jay2tall pretty much said it all. I went for a 1 GB 4870 because it could play everything I needed it to play and cost me $125 after rebate. I plan on getting something better in a couple of years when pcie 3,0 comes out and I just need something good to last until then.
If you plan to use DX11, then the 5770 makes the most sense, otherwise get the 4890.
I have a 8800GT 512mb at the moment. I have a 24" monitor which is TN panel, ans a 22" which is i-PVA. I do a bit of photoshop so would probably hook my main PC up to the 22" long term. I just wonder whether to upgrade now and sell my 8800GT on ebay which should fetch £50+, and get a 4870 1Gb for arounf £100, 48901gb for around £120, or 5770 also arounf £120. or wait another 6 months and get 58xx?
Does the 8800GT do what you want it to do now? Is your board SLI? you could always throw in a 2nd card for now and would be cheap. Honestly I have the 5870 and it is AWESOME.. so if you can wait, it may be worth it. If you are looking to upgrade now.. go for the 4890 if you can.