Solution:

We can compare the sums with almost no calculations. Choice A is eliminated since $\frac{1}{3}+\frac{1}{4}+\frac{1}{5}<\frac{1}{3}+\frac{1}{3}+\frac{1}{3}=1$ . Choice B is eliminated since $\frac{1}{2}+\frac{1}{4}+\frac{1}{6}<\frac{1}{2}+\frac{1}{4}+\frac{1}{4}=1$ . Choice D is elimianated since $\frac{1}{2}+\frac{1}{4}+\frac{1}{5}<\frac{1}{2}+\frac{1}{4}+\frac{1}{4}=1$ . Choice E is the correct one since $\frac{1}{2}+\frac{1}{3}+\frac{1}{5}>\frac{1}{2}+\frac{1}{3}+\frac{1}{6}=1$