## Final Answer

## Step-by-step explanation

Problem to solve:

Choose the solving method

The difference of the squares of two terms, divided by the difference of the same terms, is equal to the sum of the terms, in other words:

- $\displaystyle\frac{a^2-b^2}{a-b}=a+b$
- Where the value of $a$ is $x$
- and the value of $b$ is $5$, therefore:
- The fraction $\frac{x^2-25}{x-5}$ simplified equals $x+5$

Evaluate the limit $\lim_{x\to5}\left(x+5\right)$ by replacing all occurrences of $x$ by $5$

Add the values $5$ and $5$

Simplifying, we get