Antec Three Hundred

It should be no problem but anticipate no hard drives will be able to be mounted in line with the video card. I have an 8800GTX ACS3 card mounted in mine and I cant mount hard drives directly in line with it. Its no biggie for most people unless you are like me and are using it for an htpc and have several hard drives with movies, music and other data loaded on the hard drives for quick easy access...
 
The 5870 is 11 inches long. I am pretty sure it will fit if there is no HDD at the same level.

I will be receiving an Antec 300 I will put a 10.5 inch 9800 GTX+ into later this week. I will post back when I see how much room is left with my GPU in it.
 
It may not fit. My 9800 GTX+ has just about 1/2 inch before it hits the HDD rails. You might have to dremel 1/8th of an inch off the bottom hdd panel where you want to put the card.