Real reality as rhagfo is sort of implying. Is you states SP does not care a hoot about the manufactures performance/warranty ratings. You get 500 lbs per inch width of tire up to 20K lbs per axel, 34K lbs per tandem. OP WILL NEVER be over weight per those standards! That is what I get to follow in Wa St.
I also have to have a paid for license that meets or exceeds the total tonnage I am at, including both truck and trailer! That part is easy, pay the tax people! about $15 per ton of gvw I wish to be at. Hence why my sons two half tons, and my new to me as of February GM 1500 are at 8000 lbs GVW. I was overweight by 200 lbs when I went thru a scale house yesterday at 8200. Fortunately it was not open. I would have not gone thru if it were.....
Lets get to the real reality, as I mentioned in initial post after first post. Said 5W in reality, will overload the OP's truck based on most of our typical engineering specs. Yes OP can make his truck more capable, he can my more tonnage if his state allows. Reality, a DW is probably the better option. If he is like me at one time, family of 6 with 4 teenage adult sized kids, we cam in at 1200-1300 lbs depending upon cloths boots etc we were all wearing, add in bikes, firewood, canoe etc. we needed 2000-2500 lbs of payload for family, now add in 4000 or so lbs of hitch weight to the bed for the 5W, and you have the need for 6000-6500 lbs of payload. I need to be honest here. Not too many 35 series DW trucks with this amount of payload. One needs to be in the class 4 MDT relm of things.
Its one thing to add a leaf for better handling of a given load on a truck as i may do today to my 1500, or have done to many other trucks of owned, mostly 8 lug 25/35 series SW trucks, a few midgets and some mdt's. BUT OP is frankly out of his/her league with current truck for handling the total load of said trailer. That is with out spending some $4-6K in after market add ons, like new springs/coils, tires rims etc.
Marty
