#### Answer

$(-\infty,5) \cup (5,\infty)$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
The domain of the given function, $
f(x)=\dfrac{2}{x-5}
,$ is all values of $x$ for which the denominator is not $0.$ Express the answer in interval notation.
$\bf{\text{Solution Details:}}$
Since the denominator of the given function cannot be $0$, then
\begin{array}{l}\require{cancel}
x-5\ne0
\\\\
x\ne5
.\end{array}
Hence the domain is $
(-\infty,5) \cup (5,\infty)
.$