7 into 5 best min fragment found: 5/3
  Cut up 7 sticks of length 5 like this:
    2 x (7/3 + 8/3)
    2 x (2 + 3)
    3 x (5/3 + 5/3 + 5/3)
  Reassemble as 5 sticks of length 7 like this:
    1 x (5/3 + 8/3 + 8/3)
    2 x (5/3 + 7/3 + 3)
    2 x (5/3 + 5/3 + 5/3 + 2)