Start with the easy 5 x 5 magic square, where the sum of the numbers on each
row, column, and diagonal is 15.

1  2  3  4  5
3  4  5  1  2
5  1  2  3  4
2  3  4  5  1
4  5  1  2  3

You want the top row to become 5  9 13 17 21, with difference 4 and beginning
with 5.

So replace every 1,2,3,4,5, respectively, by 5,9,13,17,21, respectively.

 5  9 13 17 21
13 17 21  5  9
21  5  9 13 17
 9 13 17 21  5
17 21  5  9 13

Now the top row is an arithmetic sequence with first term 5 and difference 4.
The sum of the numbers on each row, column, and diagonal is 65.    

Edwin