I have an Itasca Spirit 31K, which is the same as the Minnie Winnie line from Winnebago. It is a lower price line than what you were looking at from Winnebago. Lower price among other things, usually means the unit will have less "stuff" and more than likely weigh less also. That being said my MH has a sticker on the door which says that I have 3,275# of OCCC. I weighed my MH with my wife and I when we had about a 3/4 tank of gas, 1/3 tank fresh water and fully loaded for camping. It weighed 11,940# with 4,120# on the 5,000# front axle and 7,820# on the 9,600# rear axle. That left us 2,560# under our GVWR of 14,500#.
As for that 5,000# hitch which is common on many of the newer class Cs, Winnebago rates mine and a number of their other lines with only a 350# tongue weight limit.