well... a stock 5850 can still do this: 1920x1200 - High settings 0xMSAA/16xAF:
Give it a OC and you ll be avg. 58 fps (5870 speed's).
Your missing out on ULTRA settings and haveing MSAA...
... if you feel thats worth blowing like 300$ on, go ahead.
And honestly what game is more demanding atm than BF3? And your card is still pretty decent for it
(though not at everything maxed out, but close there too).
And like blastingcap said.... a 7850 can reach around 580-7950 performance if you can get it running at ~1250mhz core.
It seems like most can hit over 1200mhz core judgeing by this thread:
http://forums.overclockers.co.uk/showthread.php?t=18389760
so 7850 @ 1250mhz, enjoy haveing 580 stock perf or better, for 250$.
^ probably worth it if you can find someone that bitcoin mines and wants to buy your 5850.