A mixture of good ideas and basic troubleshooting:

• Do a clean re-install of Windows. It could be that simple!
• If you don't want to re-install Windows, do a clean re-install of your drivers with ATIman, here: http://atiman.go-board.net/
• Your RAM might be bad. Run Memtest86+ overnight and make sure the RAM is alright. http://www.memtest.org/
• When you mine, do you mine one card at a time (for testing) or all at once? Instead of mining with all cards and causing BSoD, try mining with single cards at a time. See if the 3rd card alone causes the BSoD, or if the 5970's have something to do with it.
• Are you using a custom BIOS on any of your cards, by chance? Undervolting/overvolting? Underclocking/overclocking?
• Test the 3 cards you intend for this rig in a completely different rig, to make sure that the issue is definitely card related, and not related to motherboard, RAM, hard drive, or PSU.