I have seen the E05 and OL error on mine, while it was plugged in. I think what was going on was that the auto defrost cycle was happening on the fridge and it sensed it as an overload, even though it should be no more than 500 watts during defrost, and maybe 150 during regular compressor use. It has always worked though. Give the fridge some time to get through the defrost cycle, and if the error is still there, turn off the DC (battery disconnect switch) and AC (unplug your trailer from the AC power source) to perform a restart on the inverter, then try it again.
2014 Cedar Creek 36CKTS Explorer
Xantrex Freedom SW3012 inverter/charger
2009 Silverado 2500HD Duramax Crew Cab short box
Demco Glide Ride pin box
Demco Hijacker Autoslide 18K hitch