AMC 12 2003b Problem 12

What is the largest integer that is a divisor of $(n+1)(n+3)(n+5)(n+7)(n+9)$ for all positive even integers $n$?

$\text {(A) } 3 \text {(B) } 5 \text {(C) } 11 \text {(D) } 15 \text {(E) } 165$