Five thousand dollars per passenger per flight, assuming not provided by the airline for their special VVIPs?

That's more than SIN charges for their JetQuai private terminal service, including private customs/immigration/security service, or the cost at MUC including use of a private lounge room. However, my understanding is that these are private enterprises not provided by the airport itself.

OTOH, I've seen BA FC arriving passengers being escorted by staff in BA uniforms to the front of customs lines (after baggage claim) at LAX.