Factorial trailing digits

For any $N$, let $f(N)$ be the last five digits before the trailing zeroes in $N!$.

For example,

$$ \begin{aligned} &9! = 362880\ \text{so}\ f(9)=36288\ &10! = 3628800\ \text{so}\ f(10)=36288\ &20! = 2432902008176640000\ \text{so}\ f(20)=17664\ \end{aligned} $$

Find $f(1,000,000,000,000)$