"It's only five minutes"
The habit lives on small numbers. Five minutes late to a meeting, eight to the dentist, twenty to dinner. Each one seems too small to be worth anyone's concern, and when someone shows concern, you're inclined to think they're being difficult.
Let me try to show you the five minutes from the other side. What follows is my own reasoning.
Take the meeting. There are eight people in the room at nine. If you arrive at eight minutes past, you've been late by eight minutes. But the room has been carrying your absence for eight minutes multiplied by eight people. Either they started without you, and now have to go back over the first item, or they waited, and seven people lost eight minutes each. Neither is your eight minutes. Both are more.
Take the dentist. Appointments are booked back to back. Eight minutes late means the person after you starts late, and the one after them. You don't see this, because you're gone by then.
Take dinner. Dan and Ellie said half past seven. They put the lasagne in at seven, expecting it to rest and be served at eight. At ten to eight they're checking their phones, wondering whether to text, and whether the other guests would like a drink while they wait. At five to eight you arrive and say sorry, and the evening starts, and it's fine, but the first half hour of their evening was spent managing your absence.
Then there's what happens over time. Nobody minds once. After a few months, people start doing something you don't see. They plan around you. They tell you seven when they mean half past. They start without you as a matter of course. They stop asking you to pick things up on the way. Your colleague books the meeting for five past, and doesn't say why. None of this is said to your face. It's simply a set of small adjustments that other people make to your word, because your word about time has turned out to be worth less than theirs.
That, I think, is the real cost of the five minutes, and it isn't the minutes. It's that a person who is always a little late is a person whose arrival can't be relied on, and reliability is most of what people mean when they say someone is easy to deal with. You may be warm, funny and good at your job, and still be the one everyone has to work around.
There's a test of whether the five minutes matter. Notice what happens when someone is five minutes late for you. If you're honest, you notice. You look at your phone, and you feel the beginning of a small grievance, and you're pleased when they arrive, and you forgive them at once. That's exactly what happens to them.