How do I resize an image without stretching it?

Going from a 1:1 square aspect ratio to a 5:2 aspect ratio is quite a change in aspect ratio with out distortion at all you would need to crop off 60% the image or add canvas.  If you look at it this way you get a better understanding

Downsize the image from 1000x1000px to 500x500px and there will be no distortion now cut that image into two peices one 500x200 pixels leave 500x300 its a 40% 60% split

The other way is Downsize the image from 1000x1000px to 200x200px  there will be no distortion now add canvas to make the image 500x200pxb you will have what you want no distortion your whole image with a 300x200 side border

To add to the very consise and correct advice given by station_two above, there are some very tricky ways to stretch some parts and not others.  Look into Content-Aware Scaling...

http://help.adobe.com/en_US/photoshop/cs/using/WS6F81C45F-2AC0-4685-8FFD-DBA374BF21CD.html

-Noel