Not necessarily. The axle and wheel bearings can easily take the load. It is the tires that largely determine the load capacity of a pickup. If the weight on the rear axle with the trailer attached is 5000 lbs and the tires are rated at 3200 lbs. each or 6400 lbs. total you are OK. If your rear axle load exceeds the load capacity of your tires I would suggest changing the tires.
If the truck sags in the rear with the trailer load then you can add helper springs at the rear axle or go with air bags.
What people don't seem to be able to comprehend is that the load ratings are based on the weakest link of the truck as it was configured when it left the factory. I have never seen a truck on a dealer's lot that was optimized for maximum load capacity. Easier and cheaper for the factory to add two more tires and make a dually.
With all the 3/4 and 1-ton trucks the minimum load rating for any of the rear axles and wheel bearings used is 8,900 lbs. and most are rated at 10,900 lbs. and this is not the weak link as with 1/2 ton trucks.