I've got the Chevy truck in my sig with a 4x4 same engine and rear gear you have in a crewcab. My trailer weighes uder 4000 Empty and 4700 loaded. I limit by truck bed to light items like a folding table, 2-3 bikes, a couple water jugs with 1-2 gallons of water in them to keep them from blowing out and a drink cooler that goes about 40 lbs loaded. Likely in the 200 lbs in the truck bed. Myself, DW, DD and Dog go about 500 lbs between the 4 of us.
Truck pulls my camper fine. Did a Cincy-Tampa and back Trip last year down I-75 and through the Jellico Mountains. Other than wishing I had a 373 rear gear and didn't have to run at 4500 RPM's up the big hills, the truck is well matched.
Adding a thousand or two thousand lbs to what I'm pulling, My guess is it likely going to leave you feeling under powered on hills and if not properly setup, more likely to be feelign some sway and big truck passing wiggling.
If you decide to go for it, just make sure you load tongue heavy in the trailer, minimize weight in the truck bed and have good W/D and sway control installed. I won't say it's not doable and safe, just will take some work and be ready to hear that 5.3 scream going up hills.