A 5850 will certainly fit without much struggle, but a 5870 might give you some trouble, depending on the wiring. Worst case scenario you'll not be able to use (maybe even need to remove) the HDD bays right behind it.
IIRC the 5870 is ~11", and the 5850 is about 9.5".
Here's your case, and I believe the measurement is correct:
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