Suppose that $P(x)$ is a polynomial with the property such that there exists another polynomial $Q(x)$ to satisfy $P(x)Q(x)=P(x^2)$. $P(x)$ and $Q(x)$ may have complex coefficients. If $P(x)$ is quintic (i.e. has a degree of $5$) with roots $r_1, \cdots, r_5$, find all the possible values of $|r_1|+|r_2|+\cdots+|r_5|$.