5,000 pounds should be ok without a weight distribution type hitch if you don't haul a lot of cargo inside. Look at your manual it will probably state that you have a 5K rating with just the ball. You have a long wheel base so, sway shouldn't be a big deal with a utility trailer. Just balance your load. The weight will depend on what you carry in the Suburban. Try it and see. If your too nose high get the distribution hitch.
Keep in mind, passengers add a lot of weight to the rear axel, so if you haul people around, the distribution hitch will help move weight forward and will give a better ride.
I personally have not needed sway control on utility trailers, but a friction bar does not cost all that much if you end up needing one. Walmart sells reese products.