5. In a test with a full score of 100 points, all students' scores are non-negative integers. Let the scores of $n$ students be $a_{1}, a_{2}, \cdots, a_{n}$, where the number of students scoring at least $k$ points is $b_{k}$ ( $\left.1 \leqslant k \leqslant 100\right)$. Let $M=\sum_{i=1}^{n} a_{i}, N$ $=\sum_{i=1}^{100} b_{i}$, then the size relationship between $M$ and $N$ is $\qquad$ .
5. $M=N$ Detailed Explanation: On one hand, a student with a score of $k$ contributes $k$ to $M$. On the other hand, a student with a score of $k$ is counted exactly once in each of $b_{1}, b_{2}$, $\cdots, b_{k}$, and not counted in $b_{k+1}, \cdots, b_{100}$. Thus, a student with a score of $k$ also contributes $k$ to $N$, so $M=N$.