5. In a two-colored $K_{7}$, what is the minimum number of monochromatic triangles?
Solution: The minimum is 4 monochromatic triangles. A graph can be constructed to satisfy the conditions.
For $K_{8}$, the answer is 8.
For $K_{9}$, the answer is 12.
For $K_{10}$, the answer is 20.
The method is the same, calculating the number of "bichromatic angles," i.e., $\angle X Y Z$, such that $Y X, Y Z$ have different colors.

For example: Taking $K_{8}$ as a representative, let the $i$-th point connect $x_{i}$ blue edges and $7-x_{i}$ red edges.

Then the total number of "bichromatic angles" is $\sum_{i=1}^{8} x_{i}\left(7-x_{i}\right)$ $\leqslant \sum_{i=1}^{8} 3 \times 4=96$.

Since each bichromatic triangle has 2 bichromatic angles, there are at most $\frac{96}{2}=48$ bichromatic triangles, which means there are at least $\mathrm{C}_{8}^{3}-48=8$ monochromatic triangles.