May 0th

I just got this random thought.
5:00pm means 5 o'clock. The first minute in a given hour is 00 and the last is 59, that's called zero based indexing in CS world.
But the first day of a given month is, well, the 1st. So beginning of May is 05/01 not 05/00.

Why are we using zero based indexing for minutes, seconds, and hours (in the 24hr format) while using one based indexing for days and months?