1. **State the problem:** Divide the fractions $\frac{1}{8}$ by $\frac{4}{5}$. 2. **Formula:** To divide fractions, multiply the first fraction by the reciprocal of the second fraction. $$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$$ 3. **Apply the formula:** $$\frac{1}{8} \div \frac{4}{5} = \frac{1}{8} \times \frac{5}{4}$$ 4. **Multiply numerators and denominators:** $$\frac{1 \times 5}{8 \times 4} = \frac{5}{32}$$ 5. **Simplify if possible:** There are no common factors between 5 and 32, so the fraction is already in simplest form. 6. **Final answer:** $$\frac{1}{8} \div \frac{4}{5} = \frac{5}{32}$$