G5.3 If $R^{2000}<5^{3000}$, where $R$ is a positive integer, find the largest value of $R$.
$$
\begin{array}{l}
\left(R^{2}\right)^{1000}<\left(5^{3}\right)^{1000} \\
\Rightarrow R^{2}<5^{3}=125 \\
\Rightarrow R<\sqrt{125}<12
\end{array}
$$

The largest integral value of $R=11$