Ummmm
Hero, your an idiot, YOU DIDN'T FACTOR IN POWER CONSUMPTION >.<
Krachn, before you go a step further, you have to make sure your computer can also handle the physical size of the card, as well as power requirements.
So, Krachn, open your computer, look for a large greyish box near the top back, and look for a large label on it, and find the Watt rating, if it's below around 500 watts, you have to buy a new one. This list gives good brands and models:
http://www.eggxpert.com/forums/thread/323050.aspx
If your PSU has the proper wattage to handle a HD5870, you need to check if it has 2 6pin PSU connectors, should look similar to
this If it does not, you need a new PSU anyways.
Next you have to check if you can physically fit the card into your computer. Take a 12 inch ruler and try to stick it in back to front from where your PCI-E slot is, if the entire ruler doesn't fit, your screwed, need a new case at that point XD
It's a damn 11 inch card, and give another inch for the 6pin's to fit in, You MIGHT be able to squeeze in with 11.5 inches of room, but it would be tight.
So shame on you Hero, for giving someone incomplete advice, and just as a BTW, dxdiag info cannot be used to find anything like that.