Let \(f(x)\) be a polynomial with real coefficients such that \(f(0) = 1,\) \(f(2)+f(3)=125,\) and for all \(x\), \(f(x)f(2x^{2})=f(2x^{3}+x).\) Find \(f(5).\)

(第二十五届AIME2 2007 第14题)