Every month that has more than 28 days has 5 of something. Every month that has 31 days has 3 days that are repeated 5 times. There is a 1 in 7 chance that those days will be Friday, Saturday, and Sunday.

Every year has 7 months that have 31 days. Therefore, in the long run, on the average, there should be one month per year that has 5 Fridays, 5 Saturdays, and 5 Sundays.