Vakiklo :
To give a propper answer i'd have to know the full specs of your machine, the graphics card is not the only component of the pc that requires power.
However seeing as how the gtx 970 requires 145 watt and the 5970 294 watt, i'd be careful, power supplies degrade over time and might lose some of their "umpf". But i digress, please provide your full specs and i'll give you a solid answer.
Specs:
AMD FX- 6300 (Overclocked to 4.5Ghz)
AMD Radeon HD 5970
MSI 970 Gaming Motherboard
2x4 HyperX Fury 1866Mhz RAM
EVGA 500w 80+ Bronze
Samsung 850 Evo
WD Blue 1TB
Corsair H75 Water cooler.
I've got about 5 120mm case fans including my water cooler.