It depends....just to have where the 5th is currently parked, a Honda 3500 would work.
But...for when you travel it will limit you. When you get that big of a gen it will be heavy. If you travel with it in the truck bed it will likely have to stay there the entire trip. You may be able to get one in and out of the truck bed, but not me. That means you will have to run extension cords and keep the truck near the 5th. If you want to go somewhere you can't, etc.
I would get 2 Honda 2000 inverters. Run in parallel for the A/C, or one alone just for lights. Easier to move when you travel, weighs about 45#. Running one is a lot quieter. You can use it later around the house for power tools etc. Add a IPI long run tank kit for extended run time.
My gen collection: Generac 22k whole house, Generac 5k portable, Champion 3500, B&S 3k, 2 Honda 2k invertors.