1. The problem asks us to find a rational number between $5.01$ and $5.04$. 2. A rational number is any number that can be expressed as a fraction $\frac{p}{q}$ where $p$ and $q$ are integers and $q \neq 0$. 3. Since $5.01$ and $5.04$ are decimals, we can find a rational number by choosing a decimal between them with a finite decimal expansion. 4. For example, $5.02$ is between $5.01$ and $5.04$. 5. To express $5.02$ as a rational number, write it as $\frac{502}{100}$. 6. Therefore, $5.02 = \frac{502}{100}$ is a rational number between $5.01$ and $5.04$. 7. We can verify: $5.01 < 5.02 < 5.04$ is true. Final answer: $\frac{502}{100}$