Suppose $N$ is any positive integer. Add the digits of $N$ to obtain a smaller integer. Repeat this process of digit-addition until you get a single-digit number. Find the number of positive integers $N \leq 1000$, such that the final single-digit number $n$ is equal to $5$. 

Example: $N = 563 \rightarrow (5 + 6 + 3) = 14 \rightarrow (1 + 4) = 5$ will be counted as one such integer.

Let's think step by step and output the final answer within \boxed{}.
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