It's not trailer sway that's the worry with a 5er in high winds, it's the risk of tip over. I deliver new rv's and our company tells us to pull over and park if winds stay above 30mph. Funny, I don't know how a guy would ever get across Wyoming like that, maybe in the middle of the night?
Blowing over with high profile campers does happen. In fact, it's not really that rare. Our company deals with it routinely. A few years ago I was fighting 40-ish mph winds across WY, pulling over at Little America. A couple more RV haulers showed up 15-20 minutes after I did and we started visiting. They said they saw trucks blown over and the authorities were closing the interstate right behind them. Once a camper starts to go, I don't know that a dually is going to be much help over a SRW truck.
But back to the OP, a lot of guys do it. Look around at campgrounds, you usually don't have to hunt much to find big 5ers behind SRW trucks. As long as you're within the rated limits or at least close, it's definitely do-able. I've done it plenty in flatbed hauling. But when it comes to pulling something that big and heavy, I actually do prefer a dually. If you elect to stick with the SRW truck, just check out the weight on the truck's rear axle. If it's heavy and you can redistribute some of the stuff in the camper, try that. You don't necessarily need 20% pin weight for the camper to pull right. 5ers are pretty forgiving that way. If you have to redistribute weight, do so, weigh again and take it out for a short drive to see how it pulls. It'll more than likely be fine. Even 15% pin weight will likely be over 2500#, and unless you have something odd going on with your RV, that will likely work just fine.
Again, I've done plenty of it but I prefer a dually. I give up a little ride quality and mileage when empty but that's about it.