Answer
$(\frac{1}{2},\frac{1}{3})$
Work Step by Step
1. Let the two numbers be $x, y$, based on the given conditions, we can set up the following:
$\begin{cases} xy=x-y \\ \frac{1}{x}+\frac{1}{y}=5 \end{cases}$
2. Divide the 1st equation by $xy$ to get $\frac{1}{y}-\frac{1}{x}=1$,
3. Add the result to the 2nd equation to get $\frac{2}{y}=6$, thus $y=\frac{1}{3}$,
4. Use the 2nd equation again to get $\frac{1}{x}+3=5$, thus $x=\frac{1}{2}$
5. Thus, we get the solution(s) as: $(\frac{1}{2},\frac{1}{3})$
