Why not a circle of sevenths or ninths? Why fifths exactly? Without getting too deep into harmony, you should know that the fifth degree of the scale (often called the Dominant) is a pivotal point because it names the next key. So if you start at C and count up five you get to G, which is the next key. Go up five from G and you arrive at D and so on...

We have visualised The Circle of Fifths as a clockface. It is somewhat mysterious and mystical that all the keys fit neatly round the 12 hour clock. So there is a divine order in the universe! The chords in brackets are the relative minors. The most powerful chords in any key are the root (Tonic), fourth (Sub Dominant) and fifth (Dominant). You can use this diagram in a very practical way. You can see at a glance which are fundamental chords in any given key. Let's take C as an example. Go forwards five minutes and you get to G (Dominant); go back five minutes and you arrive at F (Sub Dominant). Add the relative minors and you now have six chords to play with! This procedure works at whatever point you start.