Mind Bender (10/4)

 
If you had a 6 pearl necklace, and cut it into lengths of 1, 2, and 3 pearls, you could create a 
necklace of any length from 1 to 6 pearls:  1 (1 pearl length), 2 (2 pearl length) , 3 (3 pearl length), 4 
(Connect the 1 pearl and 3 pearl lengths), 5 (Connect the 2 pearl and 3 pearl lengths), or 6 pearls 
(Connect all three lengths) .  

Q:  Similarly, suppose you have a 23 pearl necklace, and want to cut it into 5 lengths such that you 
could create a necklace of any length from 1 to 23 pearls.  How would you do it?

Difficulty level:  Reasonably challenging?

NOTE:  The first person with a correct solution gets a No Homework pass.