Say you've found places for the first $$$i$$$ knights and are looking for spots for the $$$i + 1$$$-th knight. How many of the previous knights do you actually care about in terms of where the $$$i + 1$$$-th knight can go?

The dimensions: dp[rows][3][5][5][7]

If you think you know what to do, good luck, and I recommend recursion. Create the states in a way that will make it convenient to "shift" each knight when you place another one.