As stated, 5000 lbs is the typical limit for gas chassis. However, that does not automatically mean that a diesel will pull it either. Not all diesels are created equal, so when you are shopping, you will need to pay attention. Don't just assume the fuel type will automatically solve the problem.
Also power wise, there is a lot of overlap between gas and diesel. Regardless of the fuel type, HP to weight ratio will determine your acceleration capability. The main reason diesels are rated with a higher load capacity is because they are built with greater durability. Durability and performance are not necessarily related.