Wow. Not a whole lot to help you there. Might want to follow the guidelines (link in my signature). We need to know if you need a mouse, keyboard, OS, etc. We also need to know if you can only buy from some specific stores.
Assuming you need nothing but the tower and monitor:
I changed the PSU from a 750W Corsair to the 700W OCZ. The OCZ is a little lower quality, but it's extremely nice on the budget. I also took out the HSF, which isn't necessary and can be added at any time.
If you really want to overclock, here's what you need to change:
Mobo: My build has a USB 3/SATA III board with Crossfire support. mkramer's has an older chipset that won't allow Crossfire (4x speed on the second PCIe slot).
Case: I have possibly the best case ever made. It's big enough for anything you may want to put in it (including water cooling kits and the HD 5970, not that you should get those). mkramer has a great case, but it only saves $10 and will not be ther great for expanding.
GPU: The 5850 is a good card, but is already struggling to play some games at max details at 1900x. It will get worse soon. The 5870 destroys every game at 1900x, regardless of detail setting.
RAM: I have CL 7 sticks, mkramer has CL 9 (or possibly 1333 mhz). Mine would overclock better and be faster overall.
CPU: I have a slower CPU, but the CPU doesn't affect gaming performance much. Also, it's been shown that triple core CPUs actually perform better in game (for proof search "how many cores do you need" in the articles section).
PSU: Mine isn't as high quality, but it's still a great unit. It's also extremely cheap for it's quality.
EDIT: Crap. Just noticed my build is over budget. I'll make a quick change...
You're not getting an i5 AND a 5870 on your budget. It's just not happening. With the monitor, the build I posted is the cheapest you're going to get a build with the 5870. At least not without major cuts. An i5 would add $185 (non-Crossfire board) to the build.
Typically, a second PCIe 2.0 slot allowing for 8x/8x Crossfire costs about $30. I think it's a good option to have for the future, but if you don't want it, that's alright too.
If you are absolutely sure you never want the ability to Crossfire, make this change to my build (updated from above):
EDIT: Technically, it's out now. However, the 470 is completely irrelevant. It's performance is closer to the 5850 than the 5870, while it's price ($350 MSRP, but judging by the last in stock price, $380) is closer to the 5870. Also, the extra features it has are completely useless, and will continue to be useless for several to many years.
Yes, it's a pretty case. Too bad you can't actually buy it. The guy pretty much built that himself.
EDIT: The bigger PSU needed for Crossfire would generally cost $10-20 more. However, since the build was using the OCZ 700W, that price is irrelevant, as a smaller OCZ unit would actually cost the same.
The difference is that the H55 is meant for the i3/i5 dual cores. That means it has support to boost the integreated graphics of the chips. Also, most H55 boards are micro ATX and it's rare that they have more than one PCIe slot and the added features. Unless you're building an HTPC, you should stick to the P55.