5. $n$ is the smallest positive integer satisfying the following condition:
(2) $n$ has exactly 75 positive divisors (including 1 and itself). Find $\frac{n}{75}$.
5. To ensure that $n$ is divisible by 75 and the obtained $n$ is the smallest, we can set $n=2^{\gamma_{13}} r_{2} \gamma_{3}$ and
$(r_{1}+1)(r_{2}+1)(r_{3}+1)=75$ $(r_{2} \geqslant 1, r_{3} \geqslant 2)$.

It is easy to prove that when $r_{1}=r_{2}=4, r_{3}=2$, $n$ has the minimum value. At this time, $\frac{n}{75}=2^{4} \cdot 3^{3}=432$.