Let me start with one-third rather than two-thirds.
Suppose that you have 1/3 of a mile and you want to divide it by 5, that is divide it into 5 equal lengths.
It takes 5 of these equal lengths to make 1/3 of a mile and hence it takes 5 3 = 15 such lengths to make one mile. Thus each of these lengths is one-fifteenth of a mile. Thus
1/3 divided by 5 is 1/15.
Hence 2/3 divided by 5 is 2/15.