EDIT: My only comment on your build specifically would be whether or not you really want to get a Full Tower Case.

Ive got the MSI 890fxa-gd70 as my miner board... Im using 4 slots of the 5, they're double slot cards, so you're going to have to be creative... Also I dont know if its just my board, but in a 3 card configuration, I cant get the middle card to work.Im using the Sapphire 5850s as well, just fyi.

Its configured:
Card
fan
space
Card
fan
space
Card
fan

I couldnt figure it out, but every time I tried that I saw 3 devices in device manager that were 5850s, but only 2 in catalyst/display settings. It wouldnt allow me to extend the display to enable the middle card. I did have dummy plugs, and with 4 cards in the system It works well, but this is without using the black pci-e slot. Like I said it might only be my board, but check to make sure it's able to be utilized before you dive in. 4 cards run really hot when they're all in their respective slots, so be prepared for that. My cards run 300 mhash/s each, and they run between 80 (coolest card) up to 90C (hottest card).