The 65th square

The secret of Grandmaster play is to make use of the hidden 65th square on the chess board. I'm sure you've all had the experience of having a piece come at you, apparently out of nowhere, to take one of your army. That piece came from the 65th square.

I can't show you the square, because it's not on the usual 8x8 grid system, but I can show you that it is there. Watch...

Take a 8x8 chessboard (64 squares, right?), and divide it up in a special way:

                 5             3  

8x8=64 3


             3              5  

These can be rearranged to make a rectangle. 

               5                  3                  5  

5x13=65 5

                           8                    5  

But of course, the 5x13 rectangle has 65 squares. I'm not sure which one is the extra square...

(Post inspired by Ivor Annetts, but puzzle devised by Sam Loyd, I believe.)