1. The problem is to simplify the expression $5 \frac{7}{8} - 2 \frac{2}{5}$.\n\n2. First, convert mixed numbers to improper fractions.\n$5 \frac{7}{8} = \frac{5 \times 8 + 7}{8} = \frac{40 + 7}{8} = \frac{47}{8}$.\n$2 \frac{2}{5} = \frac{2 \times 5 + 2}{5} = \frac{10 + 2}{5} = \frac{12}{5}$.\n\n3. Now subtract these fractions: $\frac{47}{8} - \frac{12}{5}$.\nFind common denominator, which is $40$ (LCM of 8 and 5).\nConvert fractions: $\frac{47}{8} = \frac{47 \times 5}{40} = \frac{235}{40}$ and $\frac{12}{5} = \frac{12 \times 8}{40} = \frac{96}{40}$.\n\n4. Perform subtraction: $\frac{235}{40} - \frac{96}{40} = \frac{235 - 96}{40} = \frac{139}{40}$.\n\n5. Convert back to a mixed number: Divide 139 by 40.\n$139 \div 40 = 3$ remainder $19$, so $\frac{139}{40} = 3 \frac{19}{40}$.\n\n6. The simplified result is $3 \frac{19}{40}$.