You have selected a pretty good build. Don't forget you need an optical drive and operating system. Do they need to be included in your budget? What is the total cost for your build system with operating system and optical drive?
Your CPU is an excellent choice.
For the video card, I recommend the GTX 460 768MB card. It is a solid card that can be found at a discount right now because it is being replaced by the GTX 550 Ti, but the new card is slower. The 768MB version of the GTX 460 is only slightly slower than the 1GB version, but costs substantially less. See the slight performance difference in this article:
Nvidia GeForce GTX 460: The Fermi We Were Waiting For : GeForce GTX 460 At 1 GB And 768 MB
That review also allows you to compare the performance of the 460 with the HD5830 you listed.
Note that on the THG Best Card for the Money article linked below, the GTX 460 1 GB is one of the cards recommended at the $200 price level. This card is almost as fast and as shown in the review above, and costs quite a bit less..
Best Graphics Cards For the Money: March 2011 : March Updates
For a specific card, I recommend the MSI Twin Frozr because of its effective but quiet heatsink/fan, factory overclock, and good price – only $130 after rebate.
Newegg.com - MSI N460GTX Twin Frozr II SOC GeForce GTX 460 (Fermi) 768MB 192-bit GDDR5 PCI Express 2.0 x16 HDCP Ready SLI Support Video Card
You can find more information about selecting video cards at:
Best Video Card Upgrades for Gaming
I assume you have confirmed that the memory you selected is compatible with the mobo - either by finding the memory on the mobo compatibility list or the mobo on the memory list generally viewable at the memory manufacturer's site.
Good choices for HDD and PSU.