If the card only supplies a max of 0.8A and the new fan requires 0.94A then it is possible that the new fan wont get enough power. If so it may not spin at all or just spin slower then it is supposed to.
Is you card still in any warranty? If so it would be better to go that route and have them replace it.
If you can't find the right fan maybe a new aftermarket cooler would be suitable? A quick search found this one that is compatable with a Radeon HD5970: http://www.arctic.ac/en/p/cooling/vga/19/accelero-xtreme-5970.html