Answer
Improper;
$1+\frac{9}{x^2-4}$
Work Step by Step
A rational expression is proper if and only if the degree of its numerator's polynomial is less than the degree of its denominator's polynomial.
Here, the degree of the numerator is $2$ while the degree of the denominator is also $2$.
Hence, the rational expression is improper.
Make the rational expression proper:
\begin{align*}
\dfrac{x^2+5}{x^2-4}&=\dfrac{x^2-4+9}{x^2-4}\\
&=\dfrac{x^2-4}{x^2-4}+\dfrac{9}{x^2-4}\\
&=1+\dfrac{9}{x^2-4}\end{align*}
