jmc

Let $a$ and $b$ be positive integers. Observe that $ab-(a+b)=(a-1)(b-1)-1$. This quantity is non-negative unless either $a$ or $b$ equals 1. Therefore, the only pairs of positive integers for which the sum exceeds the product are those of the form $\{1,n\}$ where $n$ is a positive integer. In this case, there are 4 such pairs: $\{1,2\}$, $\{1,3\}$, $\{1,4\}$, and $\{1,5\}$. There are a total of $\left(\genfrac{}{}{0ex}{}{5}{2}\right)=10$ pairs of integers, so the probability that the sum exceeds the product is $\frac{4}{10}=\boxed{\frac{2}{5}}$.