Suppose that $P(z)$, $Q(z)$, and $R(z)$ are polynomials with real coefficients, having degrees $2$, $3$, and $5$, respectively, and constant terms $3$, $1$, and $2$, respectively. Let $N$ be the number of distinct complex numbers $z$ that satisfy the equation $P(z)\cdot Q(z)=R(z)$. What is the minimum possible value of $N$?