#### Answer

No, the function $ f\left( x \right)=\frac{x+5}{x-5}$ is not continuous at $5$.

#### Work Step by Step

Consider the function $ f\left( x \right)=\frac{x+5}{x-5}$,
First check whether the function is defined at the point $ a $ or not.
Find the value of $ f\left( x \right)$ at $ a=5$,
$ f\left( 5 \right)=\frac{5+5}{5-5}$
The function is not defined at the point $5$.
Thus, the function do not satisfy the first property of being continuous.
Hence, the function $ f\left( x \right)=\frac{x+5}{x-5}$ is not continuous at $5$.