It could be almost anything, but my bet would be a standard DC jack – given that there are only two differing electrical connections to the socket via the PCB. With the five pads being the 0V and the single inner connection being the +V.
Your problem will be finding a DC jack socket with the same PCB connecting footprint.
Center to center dimensions will help find something that fits. Then, if the have the wall wart (?) power supply, it will be relatively easy to find something that is a plug in replacement.
Power supply went missing in the move too. But checked online for the product spec and found a DSS 120500 power supply, so just bought one of those with the same wattage output.
Personally, I would determine which is + and - and just run a cord off the board with the proper connector. And IF in the future you find the right connector, you can replace it.