5k inverter? As in 5000 watts? If you are going to pull 5000 watts you'll need more batteries and a way to recharge them all. Your battery setup would support a 2000 watt inverter pretty well which would power everything except an air conditioner.
I don't bother with a transfer switch, I just plug my shore power cable into the inverter 120 AC outlet. Converter is shut off at the breaker and fridge and w/h on propane.
2012 Aspen Trail 2710BH | 280 watts of solar on the roof | 2x6V GC batteries | 100% LED lighting | 1500 & 300 watt PSW inverters | so far strictly boondocking