Since $\frac{20}{19}$ is larger than 1 and smaller than 2, and $20 \times 19 = 380$, then $\frac{20}{19} < 20 \times 19 < 2019$. We note that $19^{20} > 10^{20} > 10000$ and $20^{19} > 10^{19} > 10000$. This means that both $19^{20}$ and $20^{19}$ are greater than 2019. In other words, of the five numbers $19^{20}, \frac{20}{19}, 20^{19}, 2019, 20 \times 19$, the third largest is 2019. Since the list contains 5 numbers, then its median is the third largest number, which is 2019.