If the social group in question regards 13:00 as meaning between 13:00 and 13:10 then arriving at 13:05 is arriving on time and no one is bothered or inconvenienced.
Being late is not simply a property of the clock time but also of the society you are part of.
In England arriving early for a dinner party is going to get you at least a dirty look, arriving half an hour late just means that you might miss a pre-dinner drink. In Norway, if you are ten minutes late the host might send out a search party.
"Late" here means "arriving after the social expectation." In many places in the Americas, you can be (and are expected to be) an hour "late" for a party of any kind. That doesn't mean you are late.
In a Western business context, "late" comes about 1-2 minutes after the meeting starts.
