1. **State the problem:** Simplify the expression $\frac{5}{6} - \frac{1}{3}$.\n\n2. **Recall the rule:** To subtract fractions, they must have a common denominator.\n\n3. **Find the common denominator:** The denominators are 6 and 3. The least common denominator (LCD) is 6.\n\n4. **Rewrite the fractions with the LCD:**\n$$\frac{5}{6} - \frac{1}{3} = \frac{5}{6} - \frac{1 \times 2}{3 \times 2} = \frac{5}{6} - \frac{2}{6}$$\n\n5. **Subtract the numerators:**\n$$\frac{5}{6} - \frac{2}{6} = \frac{5 - 2}{6} = \frac{3}{6}$$\n\n6. **Simplify the fraction:**\n$$\frac{3}{6} = \frac{\cancel{3} \times 1}{\cancel{3} \times 2} = \frac{1}{2}$$\n\n**Final answer:** $\frac{1}{2}$