Just to quell your worries immediately, no, there are never any puzzles which hide things from you. 5-3 has a perfectly normal solution. All I'll say is, there's something to learn in that one.
As for which place to explore next, you're free to either play the Finale puzzle right away or save it for later. Once you've completed World 6, you already know all the stuff you need to know to solve it. I think I did actually design that puzzle before I started working on most of the rest of the game, to answer that question.
Hope you continue to enjoy the game!