AMC 12 2020a Problem 4

How many $4$-digit positive integers (that is, integers between $1000$ and $9999$, inclusive) having only even digits are divisible by $5?$

$\textbf{(A) } 80 \textbf{(B) } 100 \textbf{(C) } 125 \textbf{(D) } 200 \textbf{(E) } 500$