Counting clarification for Scriabin Prelude, Op.11 No. 1

[brian healey]

I've been familiar with the piece, but never actually played it until today, and when I sat down with the score I was unexpectedly taken aback by how to properly count it. I think I've got it now, and was just thrown off by the combination of how things are written across the barline and what I assume are unmarked tuplets, but I would love some confirmation.

Am I correct in assuming the eighth notes are intended to be quintuplets and just aren't distinctly marked as such? And similarly, the LH quarter notes towards the end are intended to be triplets?