Question 2

A number not in the domain of that function would cause the value of the fraction to be $0$ or lower. Therefore, we must find the value such that $\dfrac{x-2}{x^2-5}<0.$ This yields $3$ important numbers: $2$ and $\pm\sqrt{5}.$ Observation yields that the fraction is positive for $x\in(-\sqrt{5},2)\cup(\sqrt{5},\infty)$ and non-positive (and possibly undefined) for $x\in(-\infty,-\sqrt{5}]\cup[2,\sqrt{5}].$ The largest non-positive value here is $\sqrt{5},$ whose square is $\boxed{5}$