Limits and Continuity · Hard problem

Suppose $f(2)=5$ and $\displaystyle\lim_{x\to2}\dfrac{f(x)-5}{x-2}=3$. Does $\displaystyle\lim_{x\to2}\dfrac{\bigl(f(x)\bigr)^2-25}{x-2}$ exist even though $f$ is not fully known, and if so, what is its value?