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)