A fifth degree polynomial $P(x)$ with integral coefficients. A fifth degree polynomial $P(x)$ with integral coefficients takes on values $0,1,2,3,4$ at $x=0,1,2,3,4$, respectively.
Which of the following is a possible value for $P(5)$?
A) $5$ 
B) $24$ 
C) $125$ 
D)None of the above

For example, $p\left(x\right)=x+x(x-1)(x-2)(x-3)(x-4)$.
