FWIW - I have a '06 Dodge Ram 1500 QC 2WD w/Hemi and Dodge gave it a tow rating of 7,750 lbs (assumes 150 lb driver).
I found this:
2003 Dodge Ram 1500 - Trailer Towing Specs
But according to the chart listed, in 2003 the automatic was a 4 speed, not a 5 speed.
Quad Cab™ 2WD | | | | | | | | |
GVWR | Box | Engine | Transmission | Axel Ratio | Payload | Curb Wt. | GCWR, lbs.(a) | GTWR, lbs.(b) |
6350 | 6.3 | 3.7L V-6 | Manual 5-speed | 3.55, 3.92 | 1550 | 4804 | 8000 | 3050 |
6350 | | 3.7L V-6 | Auto. 4-speed | 3.55, 3.92 | 1490 | 4863 | 8500 | 3500 |
6650 | | 4.7L V-8 | Manual 5-speed | 3.55 | 1740 | 4906 | 9500 | 4450 |
6650 | | 4.7L V-8 | Manual 5-speed | 3.92 | 1740 | 4906 | 10,500 | 5450 |
6650 | | 4.7L V-8 w/20" Tires | Manual 5-speed | 3.92 | 1680 | 4966 | 9500 | 4400 |
6650 | | 4.7L V-8 | Auto. 4-speed | 3.55 | 1700 | 4951 | 11,500 | 6400 |
6650 | | 4.7L V-8 | Auto. 4-speed | 3.92 | 1700 | 4951 | 12,500 | 7400 |
6650 | | 4.7L V-8 w/20" Tires | Auto. 4-speed | 3.92 | 1640 | 5011 | 11,500 | 6350 |
6650 | | 5.9L V-8 | Auto. 4-speed | 3.55 | 1640 | 5015 | 12,500 | 7350 |
6650 | | 5.9L V-8 | Auto. 4-speed | 3.92 | 1640 | 5015 | 13,500 | 8350 |
6650 | | 5.9L V-8 w/20" Tires | Auto. 4-speed | 3.92 | 1580 | 5075 | 12,500 | 7300 |
| | | | | | | | |
6650 | 8 | 4.7L V-8 | Manual 5-speed | 3.55 | 1550 | 5102 | 9500 | 4250 |
6650 | | 4.7L V-8 | Manual 5-speed | 3.92 | 1550 | 5102 | 10,500 | 5250 |
6650 | | 4.7L V-8 w/20" Tires | Manual 5-speed | 3.90 | 1550 | 5102 | 9500 | 4250 |
6650 | | 4.7L V-8 | Auto. 4-speed | 3.55 | 1490 | 5161 | 11,500 | 6200 |
6650 | | 4.7L V-8 | Auto. 4-speed | 3.92 | 1490 | 5161 | 12,500 | 7200 |
6650 | | 5.9L V-8 | Auto. 4-speed | 3.55 | 1400 | 5253 | 12,500 | 7100 |
6650 | | 5.9L V-8 | Auto. 4-speed | 3.92 | 1400 | 5253 | 13,500 | 8100 |
a) GCWR is the (Gross Combination Weight Rating) is the maximum allowable total weight of a fully equipped truck and trailer with cargo, driver and passengers, fuel, coolant, equipment, etc.
(b) GTWR (Gross Trailer Weight Rating) is the maximum allowable weight of the trailer and its cargo, GTWR = GCWR minus curb weight of truck minus 150 pounds (allowance for driver) and must be further decreased by the weight of optional equipment, trailer hitch, cargo, and passengers. Maximum trailer weights shown are rounded to the nearest 50 pounds. Recommended tongue weight is 10 to 15 percent of loaded trailer weight, but must not exceed 500 pounds using a bumper-mounted hitch ball (Class III trailers) or 1000 pounds using a weight-distributing receiver hitch (Class IV trailers). This requirement overrides GTWRs shown. Additionally, tongue weight should never cause vehicle to exceed GVWR (Gross Vehicle Weight Rating) or GAWR (Gross Axle Weight Rating). A weightdistributing hitch is recommended for trailers more than 2000 pounds. Use synthetic axle lubricant with the Trailer Tow Group.
Assuming the chart is correct, the max trailer weight is 6400 lbs or 7400 lbs.