Bridget has swimming lessons every 5th day and diving lessons every third day if she had swimming lesson and a diving lesson on May 5th when will be the next date in which she has both swimming and diving lessons

It'd be May 20th, because you have to the number of days between each time they overlap has to be a number divisible by both 3 and 5, and 15 is the smallest number divisible by both 5 and 3. You add 15 to 5, and get 20, so it's May 20th.