Answer
$[2, 5) \cup (5, +\infty)$
Work Step by Step
(i) The radicand (expression inside a radical sign) of a square root cannot be negative as its root is an imaginary number.
This means that the radicand in the numerator, which is $x-2$, must be greater than or equal to 0. Thus, $x$ can be any real number greater than or equal to $2$.
(ii) The denominator cannot be zero as division of zero leads to an undefined expression.
This means that the value of $x$ cannot be $5$.
From (i) and (ii) above, the restrictions to the value of $x$ are:
(i) $x \ge 2$; and
(ii) $x \ne 5$
Both of the restrictions above must be satisfied. Thus, the value of $x$ must be greater than or equal to $2$ but not including $5$.
Therefore, the domain of the given function is:
$[2, 5) \cup (5, +\infty)$
