Dodge 3500 towing heavy

You'll be over its tow rating and that could make for some slow going and possible over heating in the mountains.

Wouldn't be the first time a rig like that has hit the road with a family happily singing campfire songs all the way there and back again...

Assuming that your truck is in best possible mechanical condition with good tires that aren't too old, You'll be more than happy with it on the flat. Iowa's pretty flat isn't it?

The trailer shouldn't weigh 15,500lbs, that's just the GVWR, the capacity of the two 7000lb axles plus 1500lbs of it on the pin. Odds are it will have closer to 3000lbs on the pin just because of the way these things tend to be balanced, but a 3500 SRW should easily have 4000lbs of capacity before hitting the tire limit. It'll squat but you can get airbags for that.

Far far far more likely that you will simply be unhappy with how things handle LONG before the rig is "unsafe." With half a brain you should know it's unsafe within a few miles of your first drive. Nurse it home and address the issues.

If I remember right the older 3500 srw Dodge trucks had 6200-6500 rawr (tire/wheel/rear spring pack). Your trucks drivers side door post certification sticker has the trucks fawr/rawr.
Drop by a set of CAT scales and weigh your truck front and rear axles separately.
Subtract the CAT scale number from your trucks rawr will give you how much in the bed payload you have to work with.

Those older trucks rear axle may weigh in the 3200-3400 lbs ...subtracted from 6200 rawr = approx 3000-3300 lbs before exceeding a tire/wheel or rear suspension.

This trucks rawr will more likely be overloaded.

The '05 truck has the AAM 11.5" rear axle good for over 10k lbs so its not a concern.
And of course if its the 5.9 Cummins it won't have any issues pulling that size trailer.

Many older 350/3500 srw truck owners with heavy truck campers...heavy 5th wheel trailer hitch loads upgraded to 19.5" tires/wheels...air bags of some type of rear suspension help

For one the stock tires are 17" with a little over 3k capacity with the SRW truck. Most likely right there your tires will be overloaded. That is too much RV for that truck IMHO. Will it pull it??? YES Will it handle it??? NO

@durb thanks for the info i definitely agree that an exhaust brake is mandatory im not a full timer so i would be just camping with the truck and camper soi got a feeling that i lm going to have to get a truck with a 6.7 in it

Welcome to the forum. I have a 2004.5 3500 truck except it is a 2WD dually. It is pretty much the same truck except 10 ft-lbs less torque on mine assuming you have the 5.9 Cummins. My numbers are 21,000# GCVWR and a tow rating of 13,900#. Those numbers can be bumped 2,000# with the 4:10 rear end. These numbers say no to your trailer. However, it wouldn't bother me a bit to hook up and haul your trailer in an emergency.

I have a buddy I camp with a lot that has a 2006 2500 that pulls a large Montana most likely heavier than your trailer. His truck is lifted slightly with oversize tires and a lot of tuner goodies including a noisy 5" turbo back straight pipe and air bags. He has been towing his rig with that truck for seven years now that I know of with no chassis problems. However, he is on his third transmission with the last two being HD built with all the billet goodies and triple plate TC.

I tow 10k# to 11k# with my truck and it is a comfortable, easy tow. MY exhaust gas temperatures will rise on long steep grades. The transmission will get hot around town and on climbs slow enough to keep the torque converter out of lockup. If you have the diesel, an exhaust brake is mandatory. Did I say an exhaust brake is mandatory?

Bottom line, these are stout reliable trucks. The 48RE transmission is a weak link and is most likely a reason for the low tow ratings. I would like to have extra gears, but the 4 speed works and I have had zero issues with mine. I have about 50,000 miles on mine with the trailer hooked up.

Start by checking the door jamb for your truck's capacity.
Then check your registration for what your rig is licensed for.
Verify the current tires to see if they can handle the load.

LEGALLY? That is super simple. What is your truck registered for? That is your LEGAL gross vehicle weight rating. As long as you are under that weight loaded up to camp, you are 100% legal.

If you are OVER that weight, you simply need to pay for a higher GVWR. Then you are back to 100% legal.