## Final Answer

## Step-by-step Solution

Problem to solve:

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