Let $f$ be the following piecewise$-$defined function.

$f(x)=\{\begin{array}{ccc}{x}^2& 4\text{f}\text{o}\text{r}& x5\\ 5x& 4\text{f}\text{o}\text{r}& x>5\end{array}$

$($a$)$ Is f continuous at $x=5?$

$($b$)$ Is f differentiable at $x=5?$