To find the *exact* towing capacity for a specific 2004 Dodge Ram 1500, you need to check the sticker located on the driver's side doorjamb. This sticker will list the GVWR (Gross Vehicle Weight Rating), payload capacity, and the maximum towing capacity for that particular truck.
Without that sticker, providing a precise number is impossible and unreliable. However, you can expect the towing capacity to generally be in the range of 8,900 to 10,000 lbs but again, this is an approximation and could be higher or lower.