5. From the given six different colors, select several colors to paint the six faces of a cube, with each face painted exactly one color, and any two faces sharing an edge must be painted different colors. Then, the number of different coloring schemes is $\qquad$. (Note: If we color two identical cubes and can rotate one of them so that the corresponding top, bottom, left, right, front, and back faces of the two cubes have the same color, then we say that the two cubes have the same coloring scheme.)
5. (1) The number of ways to paint using 6 colors is $\frac{6 \times 5 \times 4 \times 3 \times 2 \times 1}{6 \times 4}=30$;
(2) The number of ways to paint using 5 colors is $C_{6}^{5} \cdot C_{5}^{1} \cdot \frac{4 \times 3 \times 2 \times 1}{4}=180$;
(3) The number of ways to paint using 4 colors is $C_{6}^{4} \cdot C_{4}^{2} \cdot \frac{2 \times 1}{2}=90$;
(4) The number of ways to paint using 3 colors is $C_{6}^{3}=20$;

Therefore, the total number of painting schemes is 320.