I'm a fellow XPS owner as well. I have an XPS 410 with a Radeon HD 5770. (awesome card by the way)
the 5770 fits in my system just fine but the studio 8000's case is slightly smaller than mine and the Radeon HD 5850 is an inch longer. So, here is what I can offer:
Your system (studio XPS 8000) dimentions from Dell
Heigth 407.75 mm (16.02 inches)
Width 185.81 mm (7.31 inches) Depth 454.57 mm (17.90 inches)
So what you would do is get a measuring tape, open up the case and measure from the I/O panel (the place where the card plate slips in) harizontally towards the front of the case and see if you have 9 1/2 inches. Remember that the 5850 will also take up the slot below your PCI-E x16 slot so you will have to have 9 1/2 inches of clearence for both slots. If you do then order away man. if not then you might want to consider a shorter card. Just incase, the 5770 is 8 1/2 inches long. and I play all the new games in highest resolution (1080i) with 3 monitors and have absolutely NO lag in Crysis 2 with maxed out settings so, if you have to get a shorter card this is the way to go.