I have this motherboard = GIGABYTE GA-990FXA-UD5
3way AMD CrossFireX and SLI multi-graphics support
You will need a powered riser for at least the fourth card, I would suggest at least two just to be safe, though. 7970's are power hungry.
Actually, I have the exactly the same setup (mobo and cards) running with 4 cards, without powered risers. Has been running stable for weeks (mining litecoin), no problem so far. I have just mailed Gigabyte customer support if its ok to plug in a fifth card... We keep you posted about the results, hehe.