5. Write a given rational number as a reduced fraction, and calculate the product of the resulting numerator and denominator. How many rational numbers between 0 and 1, when processed this way, yield a product of 20!?
5. Solution: There are 8 prime numbers within 20: $2,3,5,7,11$. $13,17,19$. Each prime number either appears in the numerator or the denominator, but not in both. Therefore, we can form $2^{\times}$ irreducible fractions $\frac{p}{q}$ such that $pq=20!$. Since in $\frac{p}{q}$ and $\frac{q}{p}$, only one lies in the interval $(0,1)$, the number of fractions that meet the criteria is $2^{7}=128$.