1. Stating the problem: Add the fractions $-\frac{5}{8}$, $\frac{5}{1}$, and $\frac{6}{5}$.\n\n2. Find a common denominator: The denominators are 8, 1, and 5. The least common denominator (LCD) is 40.\n\n3. Convert each fraction to have denominator 40:\n$-\frac{5}{8} = -\frac{5 \times 5}{8 \times 5} = -\frac{25}{40}$\n$\frac{5}{1} = \frac{5 \times 40}{1 \times 40} = \frac{200}{40}$\n$\frac{6}{5} = \frac{6 \times 8}{5 \times 8} = \frac{48}{40}$\n\n4. Add the fractions with common denominator:\n$$-\frac{25}{40} + \frac{200}{40} + \frac{48}{40} = \frac{-25 + 200 + 48}{40} = \frac{223}{40}$$\n\n5. Simplify if possible: $\frac{223}{40}$ is an improper fraction and cannot be simplified further.\n\n6. Convert to mixed number if desired:\n$$\frac{223}{40} = 5 \frac{23}{40}$$\n\nFinal answer: $\boxed{\frac{223}{40}}$ or $\boxed{5 \frac{23}{40}}$.