$\dfrac {x^2}{r^2-r-6}+\dfrac {y^2}{r^2-6r+5}=1$ will represents the ellipse, if r lies in the interval:

Given, Equation of ellipse as $\dfrac{x^2}{(r^2-r-6)}+\dfrac{y^2}{(r^2-6r+5)}=1$

For $\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1$ to be an ellipse equation$\Rightarrow a^2>0, \ b^2>0$

$\therefore (r^2-r-6)>0, \ \ \ (r^2-6r+5)>0$

$\Rightarrow (r-3)(r+2)>0, \ \ \ (r-1)(r-5)>0$

$\Rightarrow r\in (-\infty,-2) \cup (3,\infty)\;$ and $\;r\in (-\infty,1) \cup (5,\infty)$

$\therefore r\in(-\infty,-2) \cup (5,\infty)$

Options (A)