jmc

Notice that we can factor out a $5x$ from each term on the left-hand side to give $5x(x+2y)$. Similarly, we can factor out an $x^2$ from each term on the right-hand side to give $x^2(x+2y)$. Thus, we have $5x(x+2y)=x^2(x+2y)$. Since $x$ and $y$ are positive, we can safely divide both sides by $x(x+2y),$ which gives $x=\boxed{5}$.