Unregistered with IANA and not the default for any widely used software.
There is no IANA assignment for 5825 and no common product that binds to it out of the box. Ports in this stretch of the registered range are sparsely allocated, so gaps like this get picked up ad hoc by internal tools, test harnesses, and vendor agents. The only honest identification method is to look at the process holding the socket or to see what the service says when you connect.
Expose with care
No known protocol means no known authentication story. Do not open it at a firewall until you know what answers.
$ sudo lsof -nP -iTCP:5825 -sTCP:LISTENSeen this on your network? Beige Box scans your Wi-Fi and shows every open port on every device — and its Ports tool links straight back here.
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Corrections or a missing port? Reply @rimrocksystems.