The 5L is plenty of motor for what you have in mind but the 3:31 rear end is far from ideal and will dramatically reduce your real world towing comfort level. I would keep the trailers GVWR at 6 to 7,000# or less {ignore all dry weights as they are a joke}.
Your payload is good at 1780# but keep in mind even a 6,000# trailer will put 780# + another 100# for the WD hitch - a 7,000# trailer will bump that up to over 1,000#.
More than likely your truck has P rated tires which are inappropriate for towing. Moving up to LT tires will make for a huge improvement whatever you buy.
As always.... Opinions and YMMV
:C
