To divide fractions, you multiply the first fraction by the reciprocal of the second fraction.
So, to divide \( \frac{5}{8} \) by \( \frac{1}{4} \):
\[ \frac{5}{8} \div \frac{1}{4} = \frac{5}{8} \times \frac{4}{1} \]
Now, multiply the numerators and the denominators:
\[ = \frac{5 \times 4}{8 \times 1} = \frac{20}{8} \]
Now simplify \( \frac{20}{8} \):
\[ \frac{20 \div 4}{8 \div 4} = \frac{5}{2} \]
So, \( \frac{5}{8} \div \frac{1}{4} = \frac{5}{2} \).