How many digits are in the product $4^5 \cdot 5^{10}$?
$\textbf{(A) } 8 \qquad\textbf{(B) } 9 \qquad\textbf{(C) } 10 \qquad\textbf{(D) } 11 \qquad\textbf{(E) } 12$
\[4^5 \cdot 5^{10} = 2^{10} \cdot 5^{10} = 10^{10}.\]
That is one $1$ followed by ten $0$'s, which is $\boxed{\textbf{(D)}\ 11}$ digits.