Find the values of a so that the function

Given:

$f(x)=\left\{\begin{array}{l}a x+5, \text { if } x \leq 2 \\ x-1, \text { if } x>2\end{array}\right.$

We observe

$(\mathrm{LHL}$ at $x=2)=\lim _{\mathrm{x} \rightarrow 2^{-}} f(x)=\lim _{h \rightarrow 0} f(2-h)=\lim _{h \rightarrow 0} a(2-h)+5=2 a+5$

$(\mathrm{RHL}$ at $x=2)=\lim _{\mathrm{x} \rightarrow 2^{+}} f(x)=\lim _{h \rightarrow 0} f(2+h)=\lim _{h \rightarrow 0}(2+h-1)=1$

And, $f(2)=a(2)+5=2 a+5$

Since $f(x)$ is continuous at $x=2$, we have

$\lim _{\mathrm{x} \rightarrow 2^{-}} f(x)=\lim _{\mathrm{x} \rightarrow 2^{+}} f(x)=f(2)$

$\Rightarrow 2 a+5=1$

$\Rightarrow 2 a=-4$

$\Rightarrow a=-2$