SeanM

Yes. Though I'd be tempted to use 4 mm² cable at the output unless it's a very short run. 

Ignoring losses, the highest it needs to be about 5000 W for the load, plus 3000 W for the utility charger. Add 10% for losses, that's about 9000 W maximum (continuous). 9000 W / 220 V = 40.9 A. So theoretically, 40 A would be a little too low for the worst case, but usually utility charging is off or a lot less, say 1500 W. So generally, 40 A would be fine, with 6 mm² cable.
In my manual, this is called "Overload bypass". "When enabled, the unit will transfer to line mode if overload occurs in battery mode". So when the battery is providing power to the load, and the load exceeds what the inverter can supply, enabling this setting will cause the unit to switch to the utility supplying the load. Otherwise, I believe the unit would pause (no output) with a warning code 07, overload. Setting 23 is disabled by default, but would normally be enabled.
[ Edit: Clone warning is about a different setting, restart after overload. ]
[ Edit: Would likely pause with warning, not stop with error. ]