Lazy Liz divide and conquer

Algebra Level 4

Division of fractions can sometimes be tricky. Lazy Liz thinks that

$\frac{ a } { b} \div \frac{c}{d} = \frac { a \div c } { b \div d },$

because "you should just divide the numerator and the denominator". Can you tell her, how many ordered quadruples of integers $(a,b,c,d)$ are there, such that each term is between 1 and 5 (inclusive), and

$\frac{ a } { b} \div \frac{c}{d} = \frac { a \div c } { b \div d }?$