2023 AMC 12A Problem 4

Writing everything in primes, $$\begin{gathered} 8^5\cdot 5^{10}\cdot 15^5\\ {}=2^{15}\cdot 5^{10}\cdot 3^5\cdot 5^5\\ {}=3^5\cdot 2^{15}\cdot 5^{15}. \end{gathered}$$ This equals $3^5\cdot 10^{15}=243\cdot 10^{15},$ which is $243$ followed by $15$ zeros, for a total of $18$ digits. Thus, the correct answer is E.