No, it's not "unnecessary" anxiety. You need to call the powers that be and find out what the story is and explain your side. Could be your clock is slow or theirs fast or something else happened but 5 minutes isn't a lot of leeway to give yourself if you already have 2 strikes against you. It will be your word against the driver's and they can't just easily accept yours if you have already been late a couple times and the driver is a "good" one they have no reason to doubt.