The standard major diatonic scale as we think of it (Do-Re-Mi-Fa-Sol-La-Ti-Do) is a modern invention, that only came to be in Western music in the Baroque era (1600-1750). While the influence of Western music on the world has been significant, and many cultures have adopted the Western diatonic scale, it is not, nor has it ever been the standard of music throughout the world.

The music of virtually every culture on earth is based on the pentatonic scale - which is the equivalent of just playing the black keys on a piano (or Do-Re-Mi-Sol-La-Do). And the more you look through world music, the more and more you find the pentatonic scale. Traditional Chinese music is based on the pentatonic, South African folk singing, Great Highland bagpipes, even North American aboriginal singing is all based on a pentatonic scale. While some cultures have added notes to the pentatonic (such as Western classical with the major and minor diatonics), the basis of virtually all music is the pentatonic scale.

The reason for this is because the pentatonic scale contains the notes of the first notes of the overtone series. You know those tubes you could spin and they would make a whistling note, and the harder you spun, the higher the note? That's the overtone series.

So the 5 notes that Sun Tzu are referring to are the pentatonic scale.