only one i had problems with was the puzzle with the numbers and red squares, but apparently i was doing it right and the thing still said I was wrong, which is pretty damn annoying.
5-3 does NOT require a death. It's not even hard to do it... I got it on my first try. Just hit the log from the side and it will swing down and give you all the keys, then jump on it when it's spinning and jump left to get the last key. No problem!