Why do trains travel at odd times?

Why are trains always arriving and departing at something like 6:04, 5:13, times like that? To me, it doesn't make sense. Wouldn't a time like 6:30 or 5:15 be better?

well it has to do with the amount of time it takes for them to get from point a to point b...it is just like a public bus they have a schedual and they dont have the ability to go around traffic or something so they are timed and designed to go one speed and get to one place at a given time.

It is just based on travel time.

The one case where times are deliberately made at an odd hour is when a job goes to work on the graveyard shift. 12::00 midnight can create confusion regarding the calendar day, so railroads will put a crew on duty at either 11:59 PM or 12:01 AM.

Train schedules are made up with a variety of factors involved. The departure or arrival time at a major station might be some time at the top or quarter of the hour, but the other stations on the line are dependent on how long it takes the train to travel between stations.
Another consideration is the traffic on the line the train is traveling on. The trips are scheduled to eliminate one train having to wait on another to clear the way ahead.

The bottom line is that train schedules are made to keep the railroad moving, not to have station stops with a pretty time.