1. **State the problem:** Simplify the expression $5 \frac{7}{6} - 2 \frac{2}{5}$. 2. **Convert mixed numbers to improper fractions:** $5 \frac{7}{6} = \frac{5 \times 6 + 7}{6} = \frac{30 + 7}{6} = \frac{37}{6}$ $2 \frac{2}{5} = \frac{2 \times 5 + 2}{5} = \frac{10 + 2}{5} = \frac{12}{5}$ 3. **Rewrite the subtraction with improper fractions:** $\frac{37}{6} - \frac{12}{5}$ 4. **Find a common denominator:** The denominators are 6 and 5. Least Common Denominator (LCD) is 30. 5. **Convert both fractions to have denominator 30:** $\frac{37}{6} = \frac{37 \times 5}{6 \times 5} = \frac{185}{30}$ $\frac{12}{5} = \frac{12 \times 6}{5 \times 6} = \frac{72}{30}$ 6. **Subtract the fractions:** $\frac{185}{30} - \frac{72}{30} = \frac{185 - 72}{30} = \frac{113}{30}$ 7. **Convert back to a mixed number:** Divide 113 by 30: $113 = 30 \times 3 + 23$ So, $\frac{113}{30} = 3 \frac{23}{30}$ **Final answer:** $3 \frac{23}{30}$