What resolution do you game at?
Look at this article..http://www.tomshardware.com/reviews/build-balanced-platform,2469-13.html
OK it doesn't have the 5800 series cards but gives you an idea of where you are balanced. If we look at the 4890 (comparable to your 4870) we see performance gains across the spectrum (aside the ultra high resolutions) for a new CPU, wheras for your processor, the change in graphics card doesn't have so much effect, again apart from the highest resolution.
On the whole I would say its maybe time for a new CPU.