I struggled with the first 5x5 taking about 8 minutes, then 2.5 minutes, then less than one minute. I'm still not even sure what principle I'm using to solve these but it is enjoyable. It's mainly just rotating until I hit the right color and looking for the next 3+ joint to rotate.
I used to play this exact game on a mobile app. One great feature was the ability to click and hold to "lock" certain pieces into place. Like you pointed out, there's certain pieces (on the edges) that only have one possible configuration
My 5x5 is record is 28s on my 5th game. The strategy is actually really simple once you get going: run through and identify all the "lockable" (only one possible configuration) tiles and then run through the consequences of those configuration and keep repeating
