Determine the value of $x$ for which the function $f(x)=\{\begin{array}{ccc}5x,& if& x<mn>0</mn>\\ 1,& if& x=0\\ -5x,& if& x>0\end{array}$ is discontinuous.

$0$

$1$

$5$

$-5$

$-1$

None of the Above