Can you swap a five speed 01 cobra for a 6 speed?

I have a 01 cobra and the main reason I want to swap is because I think the synchros are bad. When I down shift it grinds pretty bad mostly from fifth to fourth but in the other gears as well. I figured it would just be better to get a whole new 6 speed tranny since its going to be expensive to fix regardless. I'm looking to buy the tremec t56 6 speed from American muscle. Is it possible to do the swap or would there be other things I need to swap out as well to make it work?