theres clearly something wrong if you tried a 5870 and got lower framerates.
you probably dont have the correct drivers.
here's a good guide on how to properly install them.
check back on that 5870 in two or three days.
there should be pretty hefty pricedrops prior to ati releasing the 6970. (if you want to save)
but if you want to splurge, the 6970 surely wont disappoint.
just need to install it correctly.
the system supports crossfirex, so it probably has a good psu.
i cant find the exact specs for that, however. so might be best to look it up inside.