We spend approx. 5 days away every 2 to 3 weeks, each time we come home I plug it in to keep the battery charged ? and turn off the fridge.

So if I were to leave the fridge on when we get home and plug the van into the mains for trickle charge, should I leave the fridge on Battery, Switch the Mains back on or not leave the fridge on at all?

Never too late to learn, never be afraid to ask the question

If you're storing it for a while without power, then lock the fridge door in the slightly open position. This stops it going mouldy. When storing it over winter, I open the fridge door and keep it open by opening the freezer compartment door and using it as a prop.

A thing to bear in mind is that most/all Eriba (and many other caravan fridges that run on Gas, 12V & 220V) are absorption fridges. This mean they use a heater to work.

The heaters are typically 120W (10Amps on a 12V supply) so on mains electricity every 24 hours they consume 2.9 kW/h (say 3 units) of electricity at say £0.25 per unit the fridges cost around £1 per day. Note I've rounded up numbers to £1 per day which is a little unfair but just done to point out that fridges left running when not in use can eat away at your electricity bill.

If you use a £1 per day as a guideline then you can make decisions on do I keep it running between trips or turn off, empty, leave door open to air and fire up again for next trip.

The 535 series have a condenser fridge that only runs on 12volt. If you have the van plugged in to the mains then the fridge will still run of 12 volts from the battery charger/battery.
But I would agree with the advice to turn the fridge off and prop the door open.

I'm not sure which type of system Hymer use with the 535's 12v compressor fridge. Some work off the 12v leisure battery and some have a 240v mains supply with a transformer that switches the voltage to 12v. Obviously the former will work whilst the battery has power off grid but the latter requires a hook up to operate.