While I think your tuck will tow this rig, I think you missed some things. It looks like you are figuring TOWing a trailer NOT a 5er. A 5er has pin weight of at least 1500 lbs. If you figure two persons, I would figure 450-500lbs there. Fuel weight? I had a 91 ford that hauled 34 gallons. Should figure on that, if you have the same tanks, if not, total cap of the two tanks.
As to the trailer: I guarantee you will have more weight than what you have figured.
You need to outfit the 5er with everything you will be or might be hauling-you will most likely take more than you think. Fill the truck up with fuel, hook up the 5er and take it to a scale. First weigh the combination to get your Combined Vehicle Weight (CGW), then weigh only the truck on the scales with the 5er attached, and wheels not on the scale. Now weigh the truck, again with passengers, full fuel and anything you will put in it, alone on the scale. The difference betweent the two weights is the hitch weight (how much weight the 5er puts on the TV. Now weigh the 5er alone on the scale, unhooked with the TV not on the scale. That is the trailer weight. Again, you need full water and waste tanks full, as well as anything you will put in the trailer.
I think a 350 SWD will be ok, BUT BE SURE!
Finally, look at the GCVWR (weight of both vehicles). You really should not exceed 80% of that weight. Yes, you might get away for a while, but since I had a 91 diesel and loaded it to the gills and put two trannys in it because I always ran at the max CGVWR or just over it. I learned my lesson. Don't learm fromexperience. The ride is more fun when you stay within specs.
Having said the above, you probibly won't have trouble,.