To find the length of each section when Luke cuts his board, we can divide the total length of the board by the number of sections he wants.
- We know the length of the board is \( \frac{5}{6} \) yards.
- Luke wants to cut the board into 5 equal sections.
We can represent the length of each section with the expression:
\[ \text{Length of each section} = \frac{5/6}{5} \]
Now, to simplify this expression, we can rewrite the division as multiplication by the reciprocal:
\[ \frac{5/6}{5} = \frac{5}{6} \times \frac{1}{5} \]
Multiplying the fractions, we get:
\[ \frac{5 \times 1}{6 \times 5} = \frac{5}{30} = \frac{1}{6} \]
Therefore, the length of each section is:
\[ \frac{1}{6} \text{ yard long.} \]