The CDL is needed only if the GVW of the vehicle or combination of vehicles if towing a trailer, is greater than 26,001#. Not sure about CA's weigh stations, but generally you need to stop if you're driving any vehicle with a name on the side of it (commercial) that has a GVW over 10,000#. The 5500 meets that definition, if you choose to put your name on the door. Otherwise it is a personal vehicle being used to haul your personal property. My interpretation.
A friendly phone call to CHP would get any questions answered.