I'm glad that Stanbus (on the 3rd page of posts) finally gave us some reference to the owners manual.
Yes, make sure you stay within the frontal area limit of 32 sq-ft. That uhaul link has the 5x8 trailer (floor dimensions) at 208 cubic feet. Divide that by the length (8 ft) gives you 26 sq-ft of frontal area, so you're good there.
Beyond that, the van (without the tow package) carries a 2000 lbs max tow limit. To the guy making fun of us Yanks about our class ratings, we increase numerically because you can always increase weight. If you make Class 1 = 10,000 lbs, what do you do when you want a 15,000 lb class. Nobody wants to shuffle the ratings to mean somethings new. So, class 1 is 2000, class 2 is 3500, class 3 is 5000, etc.
For this van, you have a class 3 hitch, which is rated for 5000 lbs with or without a weight distributing hitch. But the vehicle itself is only set up for 2000 lbs weight carrying. So, find out the empty weight of that trailer, subtract that weight from 2000 lbs, and that's how much weight you can put in the trailer and tow it safely.
If you put an aux cooler on it, IN MY OPINION, you can tow just fine up to the 3800 lbs tow limit. Problem is, you would need a WDH kit and functional trailer brakes (per the van's owner's manual) to go beyond 2000 lbs.
My recommendation (unless you will do much more towing in the future) is to find a smaller trailer (like a 4x8) that will weight less empty, and then load it up to 2000 lbs and be happy. That 5x8 is probably pretty heavy, and won't give you much capacity for actual stuff, given your 2000 lbs limit.