Why 5 rings..? It was designed by Baron Pierre De Courbertin(founder of the modern Olympic Movement) in 1912 after he saw a similar design on an artifact from ancient Greece. The 5 rings of the Olympic symbol represent the 5 major continents of the world: Europe, Africa, Australasia, Americas and Asia.
Why those 5 colours..? All the countries of Earth flags contain at least one of the 5 colours of the rings (Blue, Black, Yellow, Red and Green).
Why those are interlinked..? The interlinking of the rings means that everyone no matter what nationality can take part.
At the end of each Olympic Games, the mayor of that host-city presents the flag to the mayor of the next host-city. It then rests at the town hall of the next host-city for four years until the Opening Ceremony of their Olympic Games.