5. Choose several colors from the given six different colors. Color the six faces of a cube, with each face being colored with exactly one color, and any two faces sharing a common edge must be colored differently. Then, the number of different coloring schemes is $\qquad$.
(Note: If we color two identical cubes and can make the colors of the corresponding top, bottom, left, right, front, and back faces of the two cubes the same by appropriate rotation, we say that the two cubes have the same coloring scheme.)
320
5.【Analysis and Solution】Discuss by cases:
(1) The number of ways to color using six colors is $\frac{6 \times 5 \times 4 \times 3 \times 2 \times 1}{6 \times 4}=30$;
(2) The number of ways to color using five colors is $\mathrm{C}_{6}^{5} \mathrm{C}_{5}^{1} \frac{4 \times 3 \times 2 \times 1}{4}=180$,
(3) The number of ways to color using four colors is $\mathrm{C}_{6}^{4} \mathrm{C}_{4}^{2} \frac{2 \times 1}{2}=90$;
(4) The number of ways to color using three colors is $\mathrm{C}_{6}^{3}=20$.
Therefore, the total number of coloring schemes is $30+180+90+20=320$ (ways).