Let's name the two numbers $ a $ and $ b $. We want the probability that $ ab<a+b, $ $ \Rightarrow ab-a-b < 0 $, or $ (a-1)(b-1)<1 $. This inequality is satisfied if and only if $ a=1 $ or $ b=1 $. When $ a=1 $, $ b $ can equal $ 1 $ through $ 5 $, and when $ b=1 $ and $ a\not=1, $ $ a $ can equal $ 2 $ through $ 5 $. There are $ 5^2=25 $ ways to choose $ a $ and $ b, $ so the probability is $ \frac{5+4}{25}=\boxed{\frac{9}{25}} $.