The number of ways in which you can put five beads of five different colours to form a necklace is:

Number of ways of putting beads in a necklace is 4! But clockwise arrangement abcde and anticlockwise arrangement aedcb are not really different, for, the arrangement abcde gives rise to arrangement aedcb if the necklace is turned over.∴ required number of ways =12(4!)=12