I need to make a true 5x5" 300dpi image in photoshop. A friend of mine explained how to make it, but I can't remember how.

Creating a new image changing the width and height to inches, changing the resolution to 300 never makes the image true to size.

What am I doing wrong?

did you set the DPI then accept it, then go back into the image size settings and then change the size of the image?