1. The problem is to divide the fraction $\frac{5}{6}$ by $\frac{1}{3}$.\n\n2. The formula for dividing fractions is:\n$$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$$\nThis means we multiply the first fraction by the reciprocal of the second fraction.\n\n3. Applying this to our problem:\n$$\frac{5}{6} \div \frac{1}{3} = \frac{5}{6} \times \frac{3}{1}$$\n\n4. Multiply the numerators and denominators:\n$$\frac{5 \times 3}{6 \times 1} = \frac{15}{6}$$\n\n5. Simplify the fraction by dividing numerator and denominator by their greatest common divisor, which is 3:\n$$\frac{\cancel{15}^{\,5}}{\cancel{6}^{\,2}} = \frac{5}{2}$$\n\n6. The final answer is:\n$$\frac{5}{2}$$