It's all about payload. What does the yellow door sticker on your truck say about payload? Is the 6,800 lbs. you quote the dry weight or the GVWR of the trailer? (Need to use the GVWR of the trailer and about 12% of that to calculated loaded tongue weight). With half and 3/4-ton trucks, it's not about towing capacity - it's about payload. The 5.3 is a strong motor. If you don't mind 3,500 RPMs for extended periods, it's a good puller.
Use the search function on the forum and you will find many threads on weights and capacities for tow vehicles.
Rob