It takes an hour (60 minutes) for the minute's hand to turn a full circle or achieve an angular rotation of 2pi color(white)(l) "rad".
There are 60/5=12 periods of five minutes in an hour. Meaning that the five-minute rotation accounts for 1/12 of 2pi, the rotation of the minute's hand in an hour.
2 pi * 1/12=pi/6 color(white)(l) "rad" so the minute's hand shall see an angular displacement of pi/6 radians.
Dimensional analysis:
(2pi color(white)(l) "rad")/(60 color(white)(l) color(red)(cancel(color(black)("minutes"))))*5 color(white)(l) color(red)(cancel(color(black)("minutes")))=pi/6 color(white)(l) "rad"