Answer
$$
\lim _{x \rightarrow 5 } \frac{2 x-10}{x-5}=2
$$
Work Step by Step
Given $$
\lim _{x \rightarrow 5} \frac{2 x-10}{x-5}
$$
We use a table:
\begin{array}{|c|c|c|c|c|}\hline x \to5^-& {4.9} & {4.99} & {4.999} & {4.9999} \\ \hline \frac{2 x-10 }{ x-5} & {2} & {2} & {2} & {2} \\ \hline\end{array}
This means that $$
\lim _{x \rightarrow 5^-} \frac{2 x-10}{x-5}=2
$$and \begin{array}{|c|c|c|c|c|}\hline x\to5^+ & {5.1} & {5.01} & {5.001} & {5.0001} \\ \hline \frac{2 x-10 }{ x-5} & {2} & {2} & {2} & {2} \\ \hline\end{array}
This means that $$
\lim _{x \rightarrow 5^+} \frac{2 x-10}{x-5}=2
$$
Hence
$$
\lim _{x \rightarrow 5 } \frac{2 x-10}{x-5}=2
$$
