Unassigned at IANA; by VNC's 5800+display arithmetic it would be the web viewer for display :10.
IANA has no registration for 5810 and no widely deployed product claims it. The only systematic reason it appears is VNC's convention of putting the HTTP viewer at 5800 plus the display number, which makes 5810 display :10 with RFB on 5910. Display numbers that high are uncommon, so an open 5810 is at least as likely to be an unrelated in-house or vendor application. Identify it by process or by what it answers, not by the number.
Expose with care
Unregistered and unidentified. If it turns out to be a VNC HTTP listener, treat it as never-expose; otherwise find the owning process before allowing it through a firewall.
$ sudo lsof -nP -iTCP:5810 -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.