Two concerns: (1) the weight carrying capacity of the hitch receiver and (2) the carrying capacity of the axle(s). The receiver has a weight carrying rating and, on a 5000 lb Class III, it is a minimum of 500 lbs. I would not assume more unless specifically stated by the receiver manufacturer somewhere.
You will have to weigh the coach to see if the extra 843 lbs will put you over the axle GAWRs of one or both axles.. I don't know how to compute what share of the extra weight each axle will carry in your tag configuration. 50/50 maybe?
2004 American Tradition; 2014 Buick LaCRosse
Homebase in the Ocala Nat'l Forest near Ocala, FL