To divide the fractions \( \frac{5}{6} \) by \( \frac{2}{3} \), you multiply by the reciprocal of the second fraction:
\[ \frac{5}{6} \div \frac{2}{3} = \frac{5}{6} \times \frac{3}{2} \]
Now, multiply the numerators and the denominators:
\[ \frac{5 \times 3}{6 \times 2} = \frac{15}{12} \]
Next, simplify \( \frac{15}{12} \):
\[ \frac{15 \div 3}{12 \div 3} = \frac{5}{4} \]
Now, convert \( \frac{5}{4} \) to a mixed number:
\[ \frac{5}{4} = 1 \frac{1}{4} \]
So, the answer is:
1 \( \frac{1}{4} \)
Thus, the correct answer is \(1 \frac{1}{4}\).