Example 10 Let $x>y>0, xy=1$, find the minimum value of $\frac{3x^3+125y^3}{x-y}$.

Translate the text above into English, please keep the original text's line breaks and format, and output the translation result directly. 

Example 10 Let $x>y>0, xy=1$, find the minimum value of $\frac{3x^3+125y^3}{x-y}$.