1. The problem is to calculate $-16 \div \frac{8}{5}$.\n\n2. Division by a fraction is the same as multiplication by its reciprocal. So, we use the formula:\n$$a \div \frac{b}{c} = a \times \frac{c}{b}$$\nwhere $a = -16$, $b = 8$, and $c = 5$.\n\n3. Applying the formula:\n$$-16 \div \frac{8}{5} = -16 \times \frac{5}{8}$$\n\n4. Multiply the numbers:\n$$-16 \times \frac{5}{8} = \frac{-16 \times 5}{8} = \frac{-80}{8}$$\n\n5. Simplify the fraction by dividing numerator and denominator by 8:\n$$\frac{\cancel{-80}^{\times 10}}{\cancel{8}^{\times 1}} = -10$$\n\n6. Therefore, the final answer is $-10$.