Maybe it's just me, but no matter which way I approach this or try to solve it (and I've tried four different times now), I can't seem to figure out how to solve it. Is there something I'm missing here?

@Decibel - you have to guess where the first 5 is in row 1, the puzzle comes together after you have that.

SPOILER:
R1, column 7 - 11, column 15-19.

Thank you! Took me another two tries (one where I missed up an easy mistake early on and screwed me over by the end), but I got it, and I can see exactly why I went wrong. Very good and cute.

Completely logical, no spoilers needed...

I've "solved" 90% of it - just to figure out there was no logical picture on it and then find a simple error in what I've done.

Super easy to me. 100% logical. .Thanks!

Logical with a nice result. Thanks.

Perfect.