Applying alternendo on $2:5 = 6:15$ gives —

Alternendo swaps the means, exchanging the inner terms so that $\frac{a}{b}=\frac{c}{d}$ becomes $\frac{a}{c}=\frac{b}{d}$. Thus $2:5=6:15$ becomes $2:6=5:15$, and both reduce to $1:3$.