We are asked to determine the zeros of the polynomial function f(x) = 5(x + 7)^2(x - 7)^3, The zeros are determined by equating the function to zero. In this case, the function can be dissected into 5* ( x+ 7)^2 * ( x-7)^3. Hence the zeros are those numbers that make the quantity inside the parenthesis equal to zero. The zeros are -7 and +7