Is this a pretty good computer?

Id rather get a faster Samsung F3 500GB for a boot drive. The WD black 640 is noticeably slower because it has a pair of less dense 320GB platters.

Similar quality Seasonic 650W PSU for less. (Seasonic used to make the corsair 650, now its a new company)
http://www.newegg.com/Product/Product.aspx?Item=N82E16817151091

Nobody buys intel motherboards, also with an i5 760 you would normally buy a P55 motherboard, not an H55. Look for an EVGA, Gigabyte or ASUS P55 motherboard.

Given they you are looking at an i5 build, I would lean towards a GT 460 (1GB) instead of a 5830 graphics card. This is especially true if you get an SLI capable P55 motherboard as twin 460s are faster than twin 5830s.
 

There is no video on the P55 motherboard so there is no HDMI. You would get HDMI on the graphics card, not the motherboard. The specs on your graphics card are 1 HDMI, 2 DVI, 1 Miniport.
 

katiklysm

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You'll be fine with a P55 board, whether or not you can use HDMI is a function of your Graphics Card output slots- not your motherboard output slots (at least in P55 and most Motherboards), I guess some with integrated graphics may have an HDMI-Out, but who wants integrated graphics.

Disregard the comment about avoiding Intel Motherboards- they're just fine. :non:
 
They are not "fine" for self built gaming machines. They generally have a limited bios without user friendly features to help make overclocking an easy and safe process.