L$2.$ Let

$f(x)=\{\begin{array}{cc}\sqrt[\phantom{2}]{x-5}+6,& x5\\ -3,& x=5\\ x^2-15,& x<mn>5</mn>\end{array}$

Compute both

$\underset{x{5}^{+}}{lim}f(x)$

and

$\underset{x{5}^{-}}{lim}f(x)$

and using this information determine if the limit exists at $x=5.$