To solve the given limit problem, we need to evaluate:
\[
\lim_{{x \to 0}} \frac{x^2 - 10x - 25}{x^2 - 5}
\]
First, let's factorize the numerator \(x^2 - 10x - 25\) if possible.
The quadratic \(x^2 - 10x - 25\) does not factor nicely, so we will not simplify it further. We now examine the expression as \(x\) approaches 0.
Substituting \(x = 0\) directly into the expression results in:
\[
\frac{0^2 - 10 \cdot 0 - 25}{0^2 - 5} = \frac{-25}{-5} = 5
\]
Hence, the value of the limit is:
\[
\boxed{5}
\]
we will solve the quadratic equation first then put the value and know the answer ....
x= 5.....
