AHSME 1993 Problem 16

Consider the non-decreasing sequence of positive integers $$1,2,2,3,3,3,4,4,4,4,5,5,5,5,5,\cdots$$ in which the $n^{th}$ positive integer appears $n$ times. The remainder when the $1993^{rd}$ term is divided by $5$ is $\text{(A) } 0 \text{(B) } 1 \text{(C) } 2 \text{(D) } 3 \text{(E) } 4$