Example 5 In an exam with a full score of 100, $A, B, C, D, E$ five people participated in this exam. $A$ said: “I got 94 points.” $B$ said: “I scored the highest among the five of us.” $C$ said: “My score is the average of $A$ and $D$.” $D$ said: “My score is exactly the average of the five of us.” $E$ said: “I scored 2 points more than $C$ and ranked second among the five of us.” If they are all telling the truth, and everyone's score is an integer, then, how many points did $A, B, C, D, E$ each get?
Explanation: Let $b$, $c$, $d$, $e$ represent the scores of $B$, $C$, $D$, $E$ respectively. We will try to reduce the number of unknowns based on their conversation:

According to $E$'s statement, the scores of $B$, $C$, $D$, $E$ are $b$, $c$, $d$, $c+2$ respectively.

According to $C$'s statement, the scores of $B$, $C$, $D$, $E$ are $b$, $47+\frac{1}{2} d$, $d$, $49+\frac{1}{2} d$ respectively.
According to $D$'s statement, we have
$$
5 d=94+b+\left(47+\frac{1}{2} d\right)+d+\left(49+\frac{1}{2} d\right),
$$
which simplifies to $b=3 d-190$.
Thus, the scores of $B$, $C$, $D$, $E$ are
$$
3 d-190, 47+\frac{1}{2} d, d, 49+\frac{1}{2} d.
$$

Based on the ranking of their scores, we get
$$
\begin{array}{l}
3 d-190>49+\frac{1}{2} d, 49+\frac{1}{2} d>94, \\
49+\frac{1}{2} d>d .
\end{array}
$$

Solving these inequalities, we get $96 \leqslant d \leqslant 97$ (where $d$ is an integer).
Since the scores of $C$ and $E$ must also be integers, $d$ must be even. Therefore, $d=96$.
Thus, the scores of $A$, $B$, $C$, $D$, $E$ are $94, 98, 95, 96, 97$ respectively.