OIMU 2005 Problem 1

Let $P(x,y)=(x^2y^3,x^3y^5)$ , $P^1=P$ and $P^{n+1}=P\circ P^n$ . Also, let $p_n(x)$ be the first coordinate of $P^n(x,x)$ , and $f(n)$ be the degree of $p_n(x)$ . Find $$\lim_{n\to\infty}f(n)^{1/n}$$