AMC 12 2022b Problem 7

Camila writes down five positive integers. The unique mode of these integers is $2$ greater than their median, and the median is $2$ greater than their arithmetic mean. What is the least possible value for the mode?

$\textbf{(A) }5 \textbf{(B) }7 \textbf{(C) }9 \textbf{(D) }11 \textbf{(E) }13$