p6720f - upgrade video card - HP Support Forum
from looking at this post, he says you have about 9.5 inches space for your video card
standard dimensions for a gtx570 is 10.5 inches, and gtx560 ranges from around 9-10 inches... some cards may be shorter/longer depending on manufacturer as well... and if you do find a short 560, it will be a VERY tight squeeze...
but again, i m just assuming the person that wrote in the post is right about the dimensions, you should open up your computer and get the exact measurements before deciding to buy a video card.
Worst case just bring your computer to a computer shop, so you don't have to spend time doing returns and stuff if you find out the video card doesn't fit your system after buying it and any other problems that might occur (like HP setting up some blockade to force customers to buy upgrades from them).