Unassigned; VNC display :60 by convention, nothing else standard.
IANA leaves 5960 unassigned as part of the 5915-5962 block. RFB display numbering makes it :60, which is deep into the range and only reached by hosts running many simultaneous VNC sessions. Beyond that there is no registered service and no well-documented squatter.
Do not expose
Unregistered plus in the VNC block means you cannot infer safety from the number — keep it internal and check the owning process.
$ sudo lsof -nP -iTCP:5960 -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.