Before page $50$, the digit $5$ appears $5$ times.  From page $50$ to $59$, the digit $5$ appears $11$ times.  Then, the digit $5$ appears the $17$\textsuperscript{th}~time in $65$. Thus, the maximum page number is $64$. 
The pages of a book are numbered $1, 2, 3, 4, 5$, and so on. The digit $5$ appears exactly $16$ times. What is the maximum number of pages this book could have? (2019 Math Kangaroo Problem, Level 3-4, Question \#19) 

A) $$49$$ 
B) $$64$$ 
C) $$66$$ 
D) $$74$$ 
E) $$80$$ 