Answer
all real numbers apart from $-2$ and $2$.
Work Step by Step
We know that the fraction $\frac{2x+5}{x^2-4}=\frac{2x+5}{(x+2)(x-2)}$ is undefined if its denominator is $0$. By the zero product rule $x+2\ne0$ and $x-2\ne0$, hence $x\ne2$ and $x\ne-2$, hence it is continuous everywhere, apart from where it is undefined, therefore it is continuous for all real numbers apart from $-2$ and $2$.
