Strive for 65

On some highways the speed limit is 65 miles per hour. Many people retire when they're 65 years old. And 65 is the magic number in this puzzle. Pick one number from each column in the table below. Make sure no two numbers are in the same row. When you add up the five numbers you picked, the sum will always equal 65.

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

For example, you might pick the numbers 1, 10, 12, 19, and 23. Their sum is 65!

Your assignment is to explain why this happens. Your explanation should be clear enough so that anyone who reads it will easily understand why this always works. HINT: why is it so important that no two numbers you pick be in the same row or column?