If 5i is a zero then so is -5i. (Complex roots come in conjugate pairs.)
The 3rd degree polynomial has the form f(x)=a(x-4)(x²+25).
When x=2, f(x)=116, so a(-2)(29)=-58a. Therefore a=-116/58=-2.
f(x)=-2(x-4)(x²+25)=-2(x³+25x-4x²-100),
f(x)=-2x³+8x²-50x+200.