The CPU would probably be the limiting factor...the chances are the 5870 would provide only around the same performance and frame rate as a 5770 because of the CPU holding it back.
Here's some data for your reference:
Test kits: HD5870, 4GB Corsair 800Mhz DDR2, 4GB Corsair 1,600Mhz DDR3
Crysis (DirectX 10, 64-Bit, High) at 1,680x1,050
[email protected] (stock speed)=12-35fps
Q6600
[email protected]=24-45fps
[email protected] (stock speed)=19-36fps
E8400
[email protected]=27-48fps
Phenom II X4 965 BE (C3 stepping) @3.4Ghz (stock speed)=23-46fps
Phenom II X4 965 BE (C3 stepping)
[email protected] =29-52fps
Core i5
[email protected] (stock speed)=20-50fps
Core i5 750
[email protected] (stock speed)=33-57fps
(source: Custom PC Issue 078 March 2010, p41)
Unless you are going to upgrade the CPU as well, you'd probably be better off just get a 5770 instead.