Well you WILL be limited by the 1gb of Vram on your card, and quadfire scaling (especially on older cards) arent excellent.
Depending what games you will be running, but due to vram limitation and processing they won't max out modern games.
It would be a better investment to sell your older 5970 and buy a more modern card
Such as a GTX 970/r9 290/390.
-good luck