Answer
See explanations.
Work Step by Step
Step 1. Assuming a number $x$ has a rational fifth root, we have $\sqrt[5] x=\frac{m}{n}$, where $m,n$ are integers and $n\ne0$.
Step 2. We can solve $x$ to get $x=(\frac{m}{n})^5=\frac{m^5}{n^5}$
Step 3. Thus a number that has rational fifth roots must be rational and can be expressed as a ratio of two integers raised to the fifth power. We can get such numbers by letting $m,n=\pm1,\pm2,\pm3,...$ and trying different combinations.
