Wilson's Theorem/Examples/10 does not divide (n-1)!+1

Example of Use of Wilson's Theorem
For all $n \in \Z_{>0}$, $10$ is not a divisor of $\paren {n - 1}! + 1$.

Proof
For the first few $n$ we see:

Now consider $n > 5$.

We have that:

Hence $10 \nmid \paren {n - 1}! + 1$.