To be honest it probably would. The Phenom 1s weren't that fast due to AMD not being able to get the clock speed out of it. With an OC to 3.0ghz it would probably be able to feed a HD5870 just.
I wouldn't be spending the money for a new 5870 anyway, or any of the cards in fact. A new one could allow you to buy a new mobo, cpu and ram that would be miles faster. In the case of a HD6990 you can buy a new PC that would blow the socks off what you have.
What is your graphics card? An upgrade to a Phenom ii (like the 965) would be a much better choice. Something like a HD4870/ 9800GTX+/ GTS 250 and higher still has some mileage left in it.
If you were planning on getting something off ebay, get something like a HD5870 or GTX 470. You can get one for £120 ish, which isn't bad at all. I have seen some 5850s for £80 but they go quickly. To put it into context the GTX470 is about GTX560ti 448 core level, and that is £200+.