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$4.[$Differentiability$]$ Consider the piecewise function $f(x)$ given below:

$f(x)=\{\begin{array}{ccc}{x}^2-8x& 16if& x5\\ \frac{-x^{2}11x-30}{-(5-x)}& if& x>5\end{array}$

Is $f$ differentiable at $x=5?$ Justify your answer using limits$.$