Evaluate

To evaluate:

$\lim _{x \rightarrow 5} \frac{x^{2}-25}{x-5}$

Formula used:

We have,

$\lim _{x \rightarrow a} f(x)=f(a)$

As $x \rightarrow 5$, we have

$\lim _{x \rightarrow 5} \frac{x^{2}-25}{x-5}=\lim _{x \rightarrow 5} \frac{(x+5)(x-5)}{x-5}$

$\lim _{x \rightarrow 5} \frac{x^{2}-25}{x-5}=x+5$

$\lim _{x \rightarrow 5} \frac{x^{2}-25}{x-5}=5+5$

$\lim _{x \rightarrow 5} \frac{x^{2}-25}{x-5}=10$

Thus, the value of $\lim _{x \rightarrow 5} \frac{x^{2}-25}{x-5}$ is $-10$.