You can, however, add the tongue wt. back onto that figure (gvw-empty wt.), since the tongue wt. is carried by the truck, to arrive at 7700 lbs. The only way to know for sure is to weigh the trailer and see how much capacity you have left. My 16' 7K trailer weighs right at 2000 (1988#) empty, leaving me with ~5700# payload capacity. You will be pushing your trailer's wt. capacity, but if it's a factory built equipment trailer you should be fine if you check everything over carefully before you hit the road and take it kinda easy. If it's a landscape trailer, then I wouldn't try it; I'd borrow the 4.5T trailer for the move. Also, if your equipment wts. are coming from the spec sheet and not the actual wt. of the tractor as determined by weighing YOUR tractor, then I'd also borrow the 4.5T trailer.
Just watch out for the DMV guys, though I doubt they'll bother you if you're not towing commercially (unless they look at the load).
Edit: I just viewed your profile, and if you're moving the Ford 5000 that's listed, there's no way I'd try that with a 7K trailer. If it's the 3000 (guessing it's not...) then you're OK.