Answer
No vertical asymptote and $x=5\text{ is a hole}$.
Work Step by Step
If there is a rational function $f\left( x \right)=\frac{p\left( x \right)}{q\left( x \right)}$ where $p\left( x \right)$ is the numerator and $q\left( x \right)$ is the denominator then $x=a$ is a vertical asymptote of the function $f\left( x \right)$ if $x=a$ is a zero of the denominator $q\left( x \right)$.
After cancelling the common factor $x-5$ from the numerator and denominator function then,
$f\left( x \right)=x+5$
The denominator of the function $f\left( x \right)$ is a constant (there are no values of $x$ for which the denominator is equal to zero). Thus, there is no vertical asymptote.
If there is a rational function $f\left( x \right)=\frac{p\left( x \right)}{q\left( x \right)}$ where $p\left( x \right)$ is the numerator and $q\left( x \right)$ is the denominator then $x=a$ is called a hole if $x-a$ is a common factor of the numerator and denominator.
We see that $x-5$ a common factor between the numerator and denominator. So, $x=5$ is a hole.
Hence, there is no vertical asymptote and $x=5$.
