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Maximum number of 5 cell figures on an 8x8 board

I wasn't entirely sure where to post this so I guessed here would be the best place.

See the figure attached for the problem statement.

How do you go about solving a problem like this? There must some sort of proof to go along with it explaining how this undoubtedly the maximum number of 5 cell figures, right?

I'm not doing a math degree or anything so maybe this is a common type of problem in a certain area of mathematics.

Can somebody help clear things up? A start at the problem would be nice!