I think your truck will safely pull that trailer. The question is will you like the performance of it? only you can answer that.
The 5.3 is not a powerhouse of a engine and the 3.42 gear is not the greatest towing ratio.
You will be slow in the hills and the transmission will be shifting alot,make sure you have a transmission cooler.
Since you already have the truck hook it up and see if you can live with the performance of it,if not it is new truck time.
My personal opinion is I think you would be alot happier with a 6.0 liter and at least a 3.73 gear.
