Question

find a possible expression for a quadratic function with zeros -5 and 0

Answer 1

your zeros =

x = -5
x = 0

make the two functions equal zero.
1:
x = -5
add 5 to both sides
x + 5 = 0

2:
x = 0

now that you have found your two functions, simply multiply them:

x ( x + 5) = x^2 + 5x

your solution:

y = x^2 + 5x