Unassigned at IANA, immediately above the icmpd and Support Automation registrations, with nothing standard on it.
The registry assigns 5813 to icmpd and 5814 to spt-automation, and then stops — 5815 has no entry and no widely deployed default. Nothing about the number implies a protocol, so an open 5815 tells you only that some application on the host chose it. VNC's 5800+display rule would make it display :15, which is unusual enough not to be a safe assumption.
Expose with care
Unregistered and therefore unidentified from the port alone. Establish what is listening before deciding on exposure.
$ sudo lsof -nP -iTCP:5815 -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.