In the case of having someone start an appointment at 5:10 rather than 5 o'clock – I would say that the appointment was 5:10 and not 5 o'clock. For me I would just go at 5:10. I would completely skip the 5 o'clock part. But if they told me or if I made an appointment at 5 o'clock then I would be pissed off if what they really meant was 5:10.