this is getting so complicated, what with everybody talking about modes, do-re-mi and pi, whatever that is.

A pentatonic song is one that has five tones in it. They don't have to form a scale or anything else. The popularity of pentatonic tunes has to do with the fact that most people have five fingers on any one hand.

Let us say you are making a whistle for a child to play while s/he watches the cows all day. You can tell her to put her hand on a length of bamboo. You cut five holes where her fingers naturally fall, and lo you have a pentatonic flute. It won't be in any known scale, and it can't harmonize with other flutes, but it will play pentatonic tunes and will help stave off insanity while she is alone in the pasture all day (or even all summer.)

Or you can write a tune using any five notes of the scales commonly used in "Western" music.