If it's within your budget, a 6.4 would be a better choice.

I did a 29', big single slide travel trailer with my 360 Magnum and 4.10's and it struggled on 6% grades. My weight was 14,100 combined. Flat ground it was okay. The 360 has roughly the same torque numbers as the 5.7. Put any bit of wind to it and I may as well have been parked and wait it out for a calm day. Side wind and headwind absolutely tore the heart out of that 360.

But, towing an open car hauler with an E-Body on it? Don't even feel it.