They vary, even among different makes using the same graphics chipset.
I don't have good links, but I think that an 8800GT is normally 9" (229 mm) long. A Radeon 5870, 10.5" to 11"+ (267 to more than 280 mm).
Your case will determine whether the card will fit.
Also, the 5870 needs more power. The 8800GT used a single 6 pin PCI-E power connector. The 5870 uses two Six pin ones. Sapphire (www.sapphiretech.com
) also recommends at least a 500W PSU for a single 5870.