Sounds good but first you need to consider a few things:
Your going to need to upgrade your power supply to a quality 500W unit or more from a reliable manufacturer such as antec, corsair, or seasonic, buy an aftermarket cpu cooler such as the coolermaster hyper 212+ and try to oc your chip to around 3.0 ghz. Even the 5850 requires 2 6 pin pci-e connectors and an ample amount of amps on a 12v rail, (which im quite positive your stock HP power supply will not be sufficient) The 5850 would be a decent buy but you are going to need to upgrade your psu, and oc'ing your cpu wouldn't hurt things.... ( you will probably have a slight bottleneck especially on games that only utilize 2 cores although it probably will not be huge, nothing an overclock cannot resolve most likely) back to talking about gpus::: personally for the same price I would get a 6850 and oc it or go with a gtx 460 and do the same. The gtx 460 requires 2 pci-e 6 pin connectors (so does the 5850) and the 6850 only requires one. What is your monitors resolution and what games do you want to play on what settings??? Without this info it is tough to give a recommendation.
here are a couple cards you might want to look at that are pretty much on par with a 5850 (with a little oc, and these cards oc like a beast plus the 5850 is older tech although the direct cu version should allow you to oc near the 5870 so the choice is yours...)) but here are the cards
your best bet is (until you tell me your monitors resolution) probably a 6850 or gtx 460... your going to need to replace your power supply no matter what, although if you can give me the specs on your power supply as well as your monitors resolution that would be helpful, the truth is that these cards are similar in performance up to a certain point but only you can decide if the price premium is worth the performance increase, or updated feature set.....good luck and get back to me if you have any questions...
also tell me what games you play and intend on playing..?
ps: let me know if you need power supply recommendations