The expression you have is:

$x^2 - 4x - 5$

To solve for the roots of this quadratic equation, we can factor it. We are looking for two numbers that multiply to -5 and add up to -4. The numbers are -5 and +1. So we can factor the expression as:

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

Setting each factor equal to zero:

$x - 5 = 0 \quad \text{or} \quad x + 1 = 0$

Solving these gives:

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

So, the roots of the equation $x^2 - 4x - 5 = 0$ are $x = 5$ and $x = -1$.

Would you like more details on the solution, or do you have any questions?

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Here are 5 related questions you might find interesting:

1. How can you verify the roots of a quadratic equation using the quadratic formula?
2. What is the discriminant of the equation $x^2 - 4x - 5 = 0$?
3. How do you graph a quadratic equation like $x^2 - 4x - 5$?
4. What does the vertex of the quadratic equation $x^2 - 4x - 5$ represent geometrically?
5. How do you solve a quadratic equation by completing the square?

Tip: Always check if the quadratic can be factored before jumping to the quadratic formula—it might save you time!