How safe is it running a 7850 at 1200/5800 24/7 ?Almost every 7850 can do 1125MHz with a minor voltage bump, most can be pushed to 1200MHz, and if you are lucky 1250-1300MHz is reachable.
I had one that was stable at 1350MHz and could bench at 1400MHz, but I was really really lucky until a BIOS flash combined with the latest version of ASUS GPU Tweak and GPU-Z combined to bork it. My own fault for tinkering too much and pushing the ragged edge.
Aim for 1200MHz which should provide roughly 7950 stock performance.
I'm guessing as long as the temperature isn't too high then the card will have a long lifespan.