My understanding is Dometic has for several years are a " communicating " thermostat, 3 wires to AC control box . The T5000 will not work as a simple replacement. If a Coleman/Airexcell easy cheesy but I would add a 12to 3 volt transformer to power the battery terminal
Not saying impossible but would need to be a couple of relays , wireing changes , etc. You are sorta stuck with Dometic.
2012 Chevy duramax dually