What are the zeroes of y = x^2 – 4x – 5?

Start by factoring . Your two factors will be in the form (x + a) and (x + b). You want two numbers a and b to multiply to -5 and add to -4. Test out various numbers, and you'll find that -5 and 1 work! 

That means your factors are (x - 5) and (x + 1). You can double check this by foiling and seeing if you get your original equation.

Since you want to find the zeroes for that equation, that means y = 0. Remember that anything multiplied by 0 is 0, so you can set each of your factors equal to zero and solve for x. The x-values are your zeros:
x - 5 = 0
x = 5

x + 1 = 0
x = -1

-----

5 and -1