The cubic function is of the form:
f(x)=a(x+3)(x-2)(x-7), where a is a constant.
We are given that f(3)=5, so:
a(6)(1)(-4)=5,
-24a=5, so a=-5/24 and f(x)=-5(x+3)(x-2)(x-7)/24.
That is:
-5(x²+x-6)(x-7)/24=
-5(x³+x²-6x-7x²-7x+42)/24=
-5(x³-6x²-13x+42)/24=
-5x³/24+5x²/4+65x/24-35/4.