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The max trailer weight for the 2013 Ram 4.7L 6 speed are either 6450 pounds (3.55 rear axle ratio) or about 7500 pounds (3.92 ratio). I would think the tow load won't be near that.
You can look up the specific details for your truck at:
http://www.ramtrucks.com/en/towing_guide/pdf/2013-RAM.1500.Towing.Specs.pdf
You can look up the specific details for your truck at:
http://www.ramtrucks.com/en/towing_guide/pdf/2013-RAM.1500.Towing.Specs.pdf