The ATI Radeon HD 5850 is 9.50 inches (241.3mm) long. It will also fit inside the case.
For reference purposes, a standard atx motherboard is 9.60 inches wide (244 mm). The length of the 5850 and the width of the motherboard are almost the same size.
The ATI 5870 and 5970 are the two cards that will be a problem.