Mid-tower cases should fit just about every graphics card size that isn't a dual GPU, not to mention your case can also fit full-ATX motherboards, so it should fit something as long as the HD5970.
For reassurance, here's the size of your case with regards to fitting your card by Hardware Canucks: http://techwiki.hardwarecanucks.com/productimages/13942/13942_8.jpg. Based on the specification of your card, it's about 275mm long (source: http://powercolor.com/us/products_features.asp?id=311#Specification). It should be fine.