Ben visits the park every 2 days and goes to the library every 5 days. if ben gets to do both of these today, how many days will pass before ben gets to do them both on the same day again?

You could label "today" as "0."

Park every 2 days:  2, 4, 6, 8, 10, 12, 14, (etc.) days
Library every 5 days:  5, 10, 15, 20 (etc.)

You can see that the smallest number of days that must go by before Ben can do both things on one day is 10.