To evaluate \( \frac{5}{2} \div \frac{7}{4} \), we can use the rule that dividing by a fraction is equivalent to multiplying by its reciprocal. Therefore, we can rewrite the expression as:
\[ \frac{5}{2} \times \frac{4}{7} \]
Next, we multiply the numerators and the denominators:
\[ \frac{5 \times 4}{2 \times 7} = \frac{20}{14} \]
Now we need to simplify \( \frac{20}{14} \). To do this, we find the greatest common divisor (GCD) of 20 and 14, which is 2.
Now divide the numerator and the denominator by 2:
\[ \frac{20 \div 2}{14 \div 2} = \frac{10}{7} \]
Thus, the simplified answer is
\[ \boxed{\frac{10}{7}} \]