Answer the following questions. You may use the fact that $0.3 < \log_{10} 2 < 0.31$ if necessary.

\begin{itemize}
\item[(1)] Find the smallest natural number $n$ such that $5^n > 10^{19}$.

\item[(2)] Find the smallest natural number $m$ such that $5^m + 4^m > 10^{19}$.
\end{itemize}