AoPS: Don't Flip Out

Alex has 25 discs that are black on one side and white on the other. He arranges them on a 5 x 5 grid so that all the white sides are showing.

A move consists of taking any three consecutive discs in a row or column and flipping them over. You want the discs to make the checkerboard coloring shown below.

From the initial all-white position, what is the smallest number of moves needed to get to the checkerboard position?