samendoza -- Welcome to iRV2 !
Your inquiry might get better response in the special section on RV Systems / Appliances.
One thing that struck me about your post was the size of the inverter you are considering: 3 to 5 Thousand Watts ??
I believe most RV inverters are in the 500 to 1000 to 1500 to 2000 (upper end) range.
Where will you carry enough batteries to support such a load? I believe most RV inverters are in the 500 to 1000 to 1500 to 2000 (upper end) range.
To generate that much wattage, I would guess the surface area of the solar panels would be about that of a full-size house roof.
There are several threads (discussions) about solar and batteries already containing a lot of information and some very good links to sites about solar + batteries. Try using the "Find" button at the top of the discussion display.
Running the furnace (that uses propane for the actual heat) is no problem with solar re-charged batteries. However, the air-conditioning is generally out of the question (my opinion).
My signature used to include a link to my personal web-site - - - however: