Can you help me with this serieshelpmate problem? I found a different kind of problem, a serieshelpmate. I'm trying to get better by thinking outside of the box and solving different types of puzzles. So I found this one but I'm kind of stuck.
[FEN &quot;1q4Nr/4K2k/8/8/8/8/1R6/8 w - - 0 1&quot;]

Now, Black makes 5 legal moves without a reply from White. After that White gives a mate in 1. How? I am familiar with the rook and knight mate but I just can't see it.
(@NoamElkies found the source, with solution: Robert Pye, Irish Chess Union, November 2018)
I found the solution by noting that

 
 the rook can cover either one column or row
 the knight already covers f6 and h6, so it's logical to let the rook take care of the g-file
 we need the other black pieces to block the king's escape (but not being able to interpose a check by the rook)
 

It turns out that this sequence works:

 1... Kg7 2... Rh1 3... Qh2 4... Qh8 5... Rh7 6. Rg2#

You can test it in the Replayer Sandbox; it supports null moves.