The problem asks for the zeros of the quadratic function:

$x^2 - 4x - 5 = 0$

To find the zeros of this quadratic, we can factor the expression. We're looking for two numbers that multiply to $-5$ and add to $-4$.

The two numbers are $-5$ and $1$, so we can factor the quadratic as:

$(x - 5)(x + 1) = 0$

Now, set each factor equal to zero:

1. $x - 5 = 0 \Rightarrow x = 5$
2. $x + 1 = 0 \Rightarrow x = -1$

Thus, the zeros of the function are $x = -1$ and $x = 5$.

Therefore, the correct answer is:

$x = -1 \quad \text{and} \quad x = 5$

Would you like more details or explanations? Here are some related questions:

1. How can we verify the zeros of a quadratic function?
2. Can all quadratic equations be factored easily?
3. How would the quadratic formula be used to solve this problem?
4. What does it mean geometrically for a quadratic to have two real zeros?
5. How does the discriminant of a quadratic help in determining the nature of its solutions?

Tip: Always try factoring first for simple quadratics before using the quadratic formula.