For every natural number $n\geq{2}$ consider the following affirmation $P_n$: "Consider a polynomial $P(X)$ (of degree $n$) with real coefficients. If its derivative $P'(X)$ has $n-1$ distinct real roots, then there is a real number $C$ such that the equation $P(x)=C$ has $n$ real,distinct roots." Are $P_4$ and $P_5$ both true? Justify your answer.