A standard way to find limits of the form $\displaystyle \lim_{x\to a}\frac{f(x)-c^2}{\sqrt{f(x)}-c}$ where $\displaystyle \lim_{x\to a}f(x)=c^2$ is to multiply the numerator and the denominator by $\displaystyle \sqrt{f(x)}+c$ to get
$\displaystyle \frac{(f(x)-c^2)(\sqrt{f(x)}+c)}{(\sqrt{f(x)}-c)(\sqrt{f(x)}+c)} = \frac{(f(x)-c^2)(\sqrt{f(x)}+c)}{f(x)-c^2} = \sqrt{f(x)}+c$
where the latter expression does not have a singularity at $\displaystyle a$.
For this problem, use the same idea and the fact that
$\displaystyle a^3-b^3=(a-b)(a^2+ab+b^2)$ (*)
Equivalently, factor out 5 and represent x - 2 in the numerator as (x - 1) - 1 and then factor it according to (*).