Do not expect to ever be given the solution. You will only see that if and when a member posts a correct solution.

A game begins with 1.e4 and ends in the fifth move with knight takes rook mate

This is the starting position. All you have to do is enter some legal chess moves, so that the game ends on move five with knight takes rook mate. Easy enough, don't you think?

(AFAIK, composed by GM John Nunn).

I accept no responsibility for lost weekends, broken relationships or descents into madness.

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So... it could be either white or black who mates?

so we got more question than the answer.

There is no colour stipulation in the puzzle. 

can one side let the other side mate or does it have to be proper moves?

Or moves that look proper...

Wtf?? Lots of ways to do it in 6 but 5??

I have found a lot of 6's too. however there is a lot of ambiguity in the initial post which makes me suspicious. I have a feeling there might be a trick with the words or alternative interpretation.

1. "A game begins with 1.e4 and ends in the fifth move with knight takes rook mate" 
2. "All you have to do is enter some legal chess moves,"

so "ends in the fifth move" as opposed to "ends on the fifth move". I don't know if this is relevant.

Or perhaps more importantly:

"some legal chess moves" Nowhere does it state that all of the chess moves have to be legal...!

All the moves are legal and there are no tricks.

but can one side play ridiculous moves while the other side mates or do the moves have to seem playable?

I know the solution. 

All the moves are legal.... 

(Post #10)

Thank you posporov.

I give up.... lol too hard

It has to end in a forced mate right?

In descriptive notation, the last move will either be:

5. NxR#

or

5. .... NxR#

Hmmm, is it a helpmate then?