The CPU is going to hold back a HD5850 by quite a bit, although the high monitor resolution means the effect will be less pronounced than for a lower resolution.
Either: Take the plunge into the sinister and dark world of overclocking;) or drop a better CPU into the existing MB, it's capable of handling some quite good dual core units and few games benefit from more than a fast dual core anyway:http://www.asus.com/product.aspx?P_ID=6nnVb6RBxd7PhGmt
Some side notes:
That MB is Micro ATX, if it's in a small case you should check to see if the HD5850 will fit.
Overclocking will require a larger cooler, again it may not fit into a smaller enclosure so check before you take that route.
If you are still stuck in the fetid quagmire that is XP
you'll not get the DX10/11 benefits of the new card: Neither will work with XP.
If you have Vista you might want to add some more memory as well, especially if you have some or all of its memory hungry features enabled.