Here’s one way to search for a solution. Place 6 (or 5 or 7) stones on the 5x5 board, while avoiding any one-space jump or kosumi (diagonally adjacent) relationship. Then count the liberties of those stones, which represents the total number of chains that could attach to those stones, which actually represent the eventual liberties for your actual solution. This quickly rules out a liberty placement without having to check how to place chains.
If you allow more than two colors of stones, it’s very easy to color stones around a liberty arrangement to maximize the number of chains supported by those liberties.