I'm towing 5,800 dry with a 2000 Suburban 5.3 rated at 7200. I added Sumo Supersprings and an extra transmission cooler. It does fine, as long as you're not in a big hurry. I would think that the 2013 Tahoe should be able to do the job for 5,400 dry. The 5.3 will do fine. Check your weight ratings. I can't imagine that the dry weight plus 1000 will be over your limit. You may need to help out the rear suspension some. As long as your trailer brakes are in adjustment and the controller is working then stopping is not an issue. The Tahoe wheel base is a bit shorter which might affect the stability. I see Tahoes pulling campers at the beach frequently. My guess is it would do fine.
