Is $K_6$ a minor of $K_{2,2,2,2,2}$
Solution 1:
Let $a_1, a_2$, $b_1, b_2$, $c_1, c_2$, $d_1, d_2$, and $e_1, e_2$ be the 10 vertices. Vertices with the same letter are in the same partition.
Now $a_1, b_1, c_1, d_1, e_1$ form $K_5$. Now $a_2, b_2, c_2 d_2, e_2$ also forma $K_5$ and we can pick any sequence of edges so that we can contract these vertices into 1 vertex $f$. Now $f$ is connected to $a_1, \ldots, e_1$. Hence we have a $K_6$ minor.