I assumed you used GVWR incorrectly. Most people when shopping for RVs go by the "dry" weight and don't take into account the stuff they need to do more than sit in their own filth in the middle of the floor, cold, naked, thirsty and hungry all weekend.
Even at 5000lbs, your tongue weight better be at least 550lbs if not closer to 600. This will exceed the rating on the receiver, and require a WD hitch. Would an extra 100lbs break your receiver? Probably not, but do you want to chance it?
The WD hitch will still help with handling even if you don't absolutely need it.