That power supply is fully compatible with that motherboard. You obtain 24-pins by plugging in both the 20-pin and the 4-pin connectors that are located on the same cable strand.
You're going to encounter the same dilemma for your HD 5970 which requires a 6-pin and an 8-pin PCI-e connector. The power supply doesn't have any 8-pin PCI-E connectors but it does have two 6+2 pin PCI-E connectors. You connect up both the 6-pin portion and the 2-pin portion dangling from the 6-pin connector together to obtain the full 8-pins.