How would extra skilled puzzlers go about this?

We – or no less than I – would use a fixing program.

I feel you are proper: there’s seemingly no “good” human-understandable path to fixing this. The board is a 5×13 grid with 5 cells eliminated, which could be very common. That would make me suspect that the puzzle was computer-generated, even in case you hadn’t included what seems to be code output in your screenshot. And extra importantly, there is not any motive to imagine there would be a “good” resolution. Packing puzzles are onerous – in the event that they weren’t designed with a specific logical path in thoughts, it is most unlikely that they’ve one in any respect.

I agree along with your deduction concerning the cells taken up by the 5 rightmost pentominoes, however that is the one actual in-road. If we take “there may be precisely a technique to do that” as a given, we are able to rule out the 5×5 grid (as a result of if there was an answer involving it, we may rotate solely that grid to supply a distinct resolution). But then there’s nothing else you are able to do.

So, brute pressure is probably going the one choice. But I think about you are on the lookout for one thing higher than “use a pc”. If I used to be, say, locked in a room with solely pencil and paper till I solved this by hand, and informed that there’s precisely one resolution, here is what I’d do:

• Use the logic above to indicate that the “dented” form have to be appropriate.
• Calculate 12 select 5, and get 792.
• Enumerate all 792 5-subsets of the pentominoes.
• Try filling the dented sq. with every 5-subset; cross out all those that do not work. (If I’m not sure of whether or not I’ve missed something, I can choose a sure sq. to department on – have a look at all items that may fill that sq., after which check out every particular person case there.)
• When I can efficiently fill the dented-square with a 5-subset, try and pack the remaining items into the left facet of the board. It would seemingly be best to bruteforce by branching first on no matter goes into the dent (which have to be one among LINVY), after which I’d most likely choose a close-by sq. to additional department on if crucial.

It would nonetheless be a sluggish, laborious course of… however it could no less than be assured to finish finally.