the "Standard Form" of a Quadratic Equation is:

ax^2 + bx + c = 0, where a, b and c are known values and a is not 0

since the zeros are 5 and -2 the (x - 5) and (x - (-2)) are both factors of the quadratic function thus the quadratic function is:

(x - 5)(x - (-2)) = 0

(x - 5)(x + 2) = 0

x^2 + 2x - 5x - 5*2 = 0

x^2 - 3x - 10 = 0 is a quadratic function in standard form with zero 5 and -2.