$\begin{array} { l }\lim_{x \rightarrow -1^-} \left(\frac{ 5x+1 }{ x+1 }\right),\\\lim_{x \rightarrow -1^+} \left(\frac{ 5x+1 }{ x+1 }\right)\end{array}$
Evaluate the limit$\begin{array} { l }+\infty,\\\lim_{x \rightarrow -1^+} \left(\frac{ 5x+1 }{ x+1 }\right)\end{array}$
Evaluate the limit$\begin{array} { l }+\infty,\\-\infty\end{array}$
Since the left-hand and the right-hand limits are different, the limit $\lim_{x \rightarrow -1} \left(\frac{ 5x+1 }{ x+1 }\right)$ does not exist$\textnormal{Does not exist}$