8080 with a 5 bolted on: an alternate HTTP port people choose by hand.
58080 has no IANA registration — RFC 6335 keeps this range out of the registry — but its shape is not accidental. Administrators pick it as a second or third HTTP port when 80, 8080, and 8081 are already taken, so what usually answers is a servlet container, a reverse proxy, or an application's admin UI. Nmap's nmap-services lists it "unknown" at 0.000380, and SANS ISC records probes without naming a service. An HTTP HEAD request will tell you more in one second than any registry lookup.
Expose with care
If it is plain HTTP fronting an admin interface, treat it as never — cleartext credentials on an unusual port are still cleartext credentials. Put it behind TLS and authentication, or behind a VPN.
$ curl -s -m 5 -I http://TARGET:58080/Seen 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.