To evaluate the expression \( \frac{5}{2} \div \frac{7}{4} \), we can rewrite the division of fractions as multiplication by the reciprocal.
So, we have:
\[ \frac{5}{2} \div \frac{7}{4} = \frac{5}{2} \times \frac{4}{7} \]
Next, we multiply the numerators and the denominators:
\[ \frac{5 \times 4}{2 \times 7} = \frac{20}{14} \]
Now, we need to simplify \( \frac{20}{14} \). We can find the greatest common divisor (GCD) of 20 and 14, which is 2.
Now we divide the numerator and denominator by their GCD:
\[ \frac{20 \div 2}{14 \div 2} = \frac{10}{7} \]
Thus, the simplified answer is:
\[ \frac{10}{7} \]