A function g(x) is even if g(x) = g(-x) for all values of x in the domain of the function.
Also, the function is odd if g(x) = -g(-x) for all values of x in the domain of the function.
The function f(x) = x³, for example, is odd, since
f(x) = x³ = x * x * x = (-1) * (-1) x * x * x * (-1) * (-1)= - (-x)(-x)(-x) = -f(-x)
Notice that we can multiply by (-1)*(-1) since it is equal to 1 and doesn't change the other factors.
Nevertheless, the given function x³ - 5, is not odd neither even. Let's take x = 1:
f(1) = 1³ - 5 = 1 - 5 = -4
f(-1) = (-1)³ - 5 = -1 - 5 = -6
So, f(-1) ≠ f(1) and f(-1) ≠ -f(1).
Graphing this function, we can check that this function isn't even nor odd: