I can't really give a limit, but seventeen rings is obviously too much. If pressed, I suppose I would say four or five.

Seems to me that at a five-star hotel the call should be forwarded to someone else who is likely to be able to deal with the matter at hand (e.g. ringing housekeeping, forwarded to the front desk, and so on) if the call hasn't been answered after a few rings. Failing that, there ought to be a voicemail/message bank system whereby you can leave a message (although this is obviously less than ideal).

I've had similar sorts of problems at top-flight hotels, not relating to phone calls but to waiting times for some service or other –.luggage to be delivered to the room on arrival (which is why I usually try to keep it with me when checking in), a request for an iron and ironing board, that sort of thing.