Example 6 Use five different colors to color the five vertices of the "pentagram" in Figure 6 (each point is colored with one color, some colors may not be used), so that the two vertices on each line segment are of different colors. The number of different coloring methods is $\qquad$ (answer with a number).
Solution (Interval Position Classification Method): Color in the order of $A, D, B, E, C$, treating $A, B, C$ as interval positions. Since $A$, $B$, and $C$ cannot be the same color, $A, B, C$ can only be colored with 3 colors or 2 colors. When $A, B, C$ are colored with three colors, there are $3 \times 2 \times \mathrm{A}_{5}^{3}=540$ coloring methods; when $A, B, C$ are colored with two colors, there are $4 \times 3 \times 2 \times \mathrm{A}_{5}^{2}=$ 480 coloring methods. Therefore, there are a total of $540+480=$ 1020 coloring methods that meet the conditions.

Comment: This problem can also be solved using the color number classification method.