For the second round of the Mathematical Olympiad, 999 students are invited. Melanie creates invitation letters in order of participant number: $1, 2, 3, \ldots$. For some values of $n \geq 100$, she notices the following: the number of participant numbers from $1$ up to and including $n$ ending in a $5$ is exactly equal to the integer formed by the last two digits of $n$.
For how many values of $n$ (with $100 \leq n < 1000$) does this hold?