There are many solutions to this POW. One way is called BRUTE FORCE. This way is to count each one. To do this, make a list of all of the rectangles with the dimensions 1x1, 1x2, 1x3, 1x4, 1x5, then do the 2x1, 2x2, ect. You can find great patterns in these as well.
or
Find a pattern for each row and column and use multiplication.
or
Find how many rectangles are in a 1x1 square, a 2x2 square, a 3x3 square - use this pattern to determine how many are in a 5x5 square.