Put number 1 in the middle of the top row. Put the numbers 2 up to n (= length of the square) each time one cell diagonal up and to the right. Put number n+1 below number n. Put the numbers n+2 up to 2n each time one cell diagonal up and to the right. Put number 2n+1 below number 2n. Etcetera ...

5x5 symmetric magic square

You can use this method to construct magic squares of odd order from 3x3 to infinite and you get symmetric (but not pan)magic squares.

See 3x3, 5x5, 7x7, 9x9, 11x11, 13x13, 15x15, 17x17, 19x19, 21x21, 23x23, 25x25, 27x27,  29x29 and 31x31