5. 75 Detailed Explanation: Using one color, there are $C_{6}^{1}$ different ways to color; using two colors, there are $C_{5}^{2} \times 3=30$ ways to color; using three colors, there are $C_{5}^{3} \times 3=30$ ways to color; using four colors, there are $C_{5}^{4} \times 2=10$ ways to color, for a total of 75 ways to color.
5. Use 5 different colors to paint the faces of a regular tetrahedron, with each face painted one color, and no face left unpainted. The number of different coloring methods is $\qquad$.

