7. 1020 Detailed Explanation: Convert it into a coloring problem of a circular disk with five sector cells, each to be colored with one of five colors, such that no two adjacent cells have the same color. Let the number of ways to color a circular disk with $k$ sector cells using five colors be $x_{k}$, then we have $x_{k}+x_{k-1}=5 \cdot 4^{k-1}$. Therefore, $x_{5}=\left(x_{5}+x_{4}\right)-\left(x_{4}+x_{3}\right)+\left(x_{3}+x_{2}\right)-x_{2}=5\left(4^{4}-4^{3}+4^{2}-4\right)=1020$.
7. Use five different colors to color the five vertices of the "pentagram" in the figure (each vertex is colored with one color, and 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 $\qquad$.