Maybe they noticed the pattern in the two terms. Try differentiating f(x) = e<sup>-5x</sup>. What do you get?
So if you have ye<sup>-5x</sup> = 0, what will you get if you differentiate implicitly with respect to x?
Eliz.
P.S. I'm not saying that this is "the" way to do it, but, until somebody comes along with a proper methodology, this at least gives you a hint of a possibly-useful way to look at things.