+1 what jsc said.
Unlike the rest of the ATI radeon HD 5000 series video cards, the 5970 is a power hog.
There appears to be a misunderstanding about multiple +12 volt rails. True multiple +12 volt rails were designed for very high end, very high wattage power supplies. There are only a few of them.
With one exception, the lower wattage power supplies do not have true multiple +12 volt rails. Instead, think of them as "virtual rails". It was an advertising gimmick to increase sales. There was a big stink about it a few years ago.
If you would like to learn more about multiple +12 volt rails, then here is a link to an excellent explanation at jonnyguru.com:http://www.jonnyguru.com/forums/showthread.php?t=3990