Consider the following statements regarding the function f(x) =...

Given the function $f(x) = \dfrac{1}{x - 5}$.

Differentiating with respect to $x$, we get:
$f'(x) = \dfrac{d}{dx}(x - 5)^{-1} = -1(x - 5)^{-2} = -\dfrac{1}{(x - 5)^2}$

For all $x \neq 5$, $(x - 5)^2 > 0$, which implies $f'(x) < 0$.

Since $f'(x) < 0$ for all $x \neq 5$, the function $f(x)$ is strictly decreasing on the interval $(-\infty, 5)$ and strictly decreasing on the interval $(5, \infty)$.

Therefore, Statement-I is correct.

Statement-II claims that $f'(x) > 0$ for all $x \neq 5$, which contradicts our finding that $f'(x) < 0$. Thus, Statement-II is not correct.

Hence, Statement-I is correct but Statement-II is not correct.

Answer: Statement-I is correct but Statement-II is not correct