I see two main advantages:
1) It is much easier to divide in three than in five, which means
that the most important part of the division is more fairly done.
2) The bread get dry more slowly when in large pieces. (Or
generally: food is better conserved when in large pieces). In this
example, you start eating the 1/15 and save the 1/3 till later.
Today, we see advantages when dividing two pizzas between seven people:
Instead of dividing each of the pizza in seven parts (which is not
easy), we divide each in four (which is easy). The part left is either
divided further, or eaten by the hungriest person. This actually adds
flexibility.
(I hope these comments did not break the rules of the list - I know
they were not based on thorough research, or indeed research at all...)
Bjørn Smestad
Assistant professor
Finnmark College, Norway