Sophia I checked, for the LH I do indeed play 3-5 on B G in measure one, then 5 on that A. Then in measure two I play that C with 3. And this fingering is basically the same as I what I play in the next section (starting in measure 9).
@Sophia you already know a lot about fingering but I’ll share my thoughts here, since I do believe fingering choices go beyond just personal preference.
So fingering in general … when a piece calls for legato (as this one does), fingering should contribute to making legato playing easier and more effective (i.e. more legato). By that standard, you would think that the best fingering choice would be 3-5 on Bb G, then 4 on the A. Also looking at how the piece is written, we should be holding that G. So that’s the fingering I tried first. But I didn’t like how it felt.
This leads to another general rule of fingering, which is that it should contribute to smoothness and feel comfortable. Since I have a lot of problems with my tendons, I’m always trying to prioritize fingering that lets me keep my hand as relaxed possible, and fingering that avoids unnecessary stretches. And if I can release a stretched out hand position more quickly, whether it’s by a fingering choice or by using the pedal, then I generally do that, because it keeps my hands happy. But choosing fingering based on whether it feels comfortable or not is tricky because sometimes a fingering doesn’t feel comfortable at first but quickly becomes comfortable after you play into it a bit. But again, we can use the pedal here, so my take is, why do something that doesn’t feel right and might be a strain on my hands when I have the pedal (piano mechanics) to make up for it. Also, in my case, the stretch between 4 and 5 isn’t so bad, the stretches that give me trouble are ones that involve the thumb (because I have de quervain’s tenosynovitis in both hands), so playing Bb G with 4-5 is fine in general, but it’s not great in this piece because you need to get to that A, which in the middle there. (I need to go back look at his fingering actually because I’m curious why he did that).
Another fingering principle that I follow is that fingering should be not only the same for the same notes (e.g., in this piece, same Bb G in measures one and two means same 3-5 pattern in both measures), but also when it’s the same hand shape or same interval, esp. when one interval moves into another with the same progression, then it should be the same fingering through the piece. And of course we should be playing with the same fingering throughout each time we play the piece, because this contributes to memorizing the piece. So this is like two types of consistency, one in terms of just playing with the same fingering every time we play that piece and the other is using the same fingering patterns across trajectory of a piece.
The next fingering principle is perhaps the hardest one for beginning and intermediate pianists like us, and that is that fingering should not only contribute to speed, accuracy, and smoothness (for example, there a different fingering patterns for trill and for repeated thirds etc that may seem counterintuitive but actually allow you to move your hand/dingers faster) but fingering should also contribute to musicality. For example, bringing out one note more than others etc. My teacher will sometimes suggest fingering I hadn’t considered, often either because it’s mechanically better or it’s musically better.
So in summary, here are the principles I follow when selecting fingering:
Consistency
Legato
Smoothness and comfort
Hand mechanics
Musicality
I should ask my teacher about this and see if she thinks anything is missing from this list.