Answer
$a_n=\frac{3n+2}{n!}$
Work Step by Step
We can see that the subsequent terms' numerators' differences are $3$ and the denominators follow the formula $n!$. $a_1=\frac{5}{1}=\frac{5}{1!}$, so $a_n=\frac{3n+2}{n!}$ for all $n$ natural numbers.