### Instruction: Solve the inequality
\[\frac{x^2 - 25}{x + 5} < 0.\].### Response: I see a quadratic expression in the numerator and a linear expression in the denominator, so I want to factor them and see if I can simplify the fraction.
The numerator can be factored as a difference of squares: \[x^2 - 25 = (x - 5)(x + 5).\]
The denominator is already in factored form, so I can write the fraction as \[\frac{(x - 5)(x + 5)}{x + 5}.\]
Now I notice that the factor $(x + 5)$ appears in both the numerator and the denominator, so I can cancel it out as long as it is not zero.
This means that $x \neq -5$, because if $x = -5$, then the fraction would be undefined.
So I can simplify the fraction to \[\frac{x - 5}{1} = x - 5.\]
Now the inequality becomes \[x - 5 < 0.\]
This is a very simple linear inequality, and I can solve it by adding 5 to both sides: \[x < 5.\]
This is the solution, but I have to remember to exclude the value $x = -5$, because it makes the original fraction undefined.
So I can write the final answer using interval notation or set notation.