I can't even begin to think how Nunn came up with this puzzle; it isn't really composed, but inherent in the initial position in chess. I can personally assure you that it is possible (you may still not believe it), as I finally figured it out after many hours of staring at it
Man do i hate these puzzles where a bazillion moves are possible....
Haven't looked at it closely yet but somehow that "knight takes rook mate" is hiding something... Like a discovery where another piece actually mates the king. That piece would probably be a queen or a bishop which could mean that a pawn has to move. The thing is, you have to throw every chess principle you know for this puzzle. Finding the worst possible move is the key.
There are multiple mates in less than 4 moves but getting one in 5 where the 5th move is NxR....That is one annoying problem
The solution can be worked out logically, by deducing ways which cannot work, and thus realising the only possible way to mate. However it is a bit harder to actually find the solution than this (although it really shouldn't be) and when you figure it out, you will probably wonder why it took so long to find given its apparent simplicity.