To divide the fractions \( \frac{5}{8} \) by \( \frac{3}{4} \), we can multiply by the reciprocal of the second fraction.
So, we have:
\[ \frac{5}{8} \div \frac{3}{4} = \frac{5}{8} \times \frac{4}{3} \]
Now, perform the multiplication:
\[ \frac{5 \times 4}{8 \times 3} = \frac{20}{24} \]
Next, simplify \( \frac{20}{24} \):
\[ \frac{20 \div 4}{24 \div 4} = \frac{5}{6} \]
So, \( \frac{5}{8} \div \frac{3}{4} = \frac{5}{6} \).
Therefore, the answer is \( 5/6 \).