No DC Loads?
I’m assuming this is 4 X 12 volt batterie sin series for 48 volts with a 100 amp fuse. May be a little small if the total inverter wattage is 5000 watts. That 5000 watts would not include the inverter loss. My smaller inverters are around 15%. May need 125 amp or 150 amp fuse.
EDIT: DISREGARD Earlier comment the schematic is correct