I cannot figure out how I should play the left-hand arpeggio in beats 3-4 of this bar:
(Nuvole bianche Bar 54)
Currently I use this fingering for the first arpeggio:
But I have no idea how to play the second arpeggio. What fingering should I use to be able to perform this arpeggio at speed?
Your proposed 5 2 1 2 1 2 breaks the basic "rule" of scale and arpeggio fingering, which is your thumb always plays a white note - unless there are no white notes at all, of course.
Note: of course that rule doesn't apply to the right hand - the Eb Ab C is not really an arpeggio, it's just a 3-note chord, and there is no problem fingering it 5-1-3, 4-1-2, or something similar (4-1-2 might be appropriate if the top note of the preceding bar was higher than Eb).
So the LH "top notes" C and G should definitely be played with your thumb. The easiest way to play the rest is not to worry about trying to play the notes perfectly "legato" with your fingers. Press the sustain pedal as you play the first note of each chord (the low Ab and Eb). It's up to you whether you release the pedal as soon as it's no longer needed, keep it down for the whole of each half-bar, or something in between those extremes.
With the pedal, the fingering will be 5-x-y 1-y-x 5-x-y 1-y-x, where "x" and "y" depend on the size of your hand.
If your hands are very small, you might want to play 5-5-3 1-3-5 5-5-3 1-3-5, moving your hand and arm to play the consecutive notes with 5. That is a better way than trying to twist your hand about to play the notes legato with your fingers.
With an average adult-sized hand and reasonably flexible fingers, 5-3-2 1-2-3 5-3-2 1-2-3 would be good, again not trying to play the 5-3's and 3-5's legato but using the sustain pedal. In between those limits, experiment with 5-3/4-2/3 1-2/3-3/4 to find what suits you best.
While there is a "rule" that one shouldn't play black notes with the thumb, it isn't a hard-and-fast rule. The hard-and-fast rule is that you should use whatever fingering most easily plays the music you're trying to play. The reason that the scales (and all the arpeggios that don't have all black keys) never use the thumb on black keys is because there are always easier fingerings available.
In general, you should avoid passing the fingers and thumbs over one another in broken chord passages when possible, since (as alephzero also mentions) it's more awkward than stretching or even jumping a bit to make notes.
In a widely-spaced figure such as the one in the left hand, don't try too hard to connect all the notes. As you have found, you can't without a lot of awkward reaching around, and that gets in the way of playing at any kind of fast tempo. So, I simply finger them 532123 532123, and suggest that you try it as well. You'll have to get proficient at jumping an octave between 3 and 5 as part of your technical repertoire anyway, so you might as well get started. (If your hands are too small to reach a 4th with 23, then jump a little there as well.)
It's easy to get caught up in trying to work out fingerings that allow you to connect all the notes without using the pedal. While this is a good idea up to a point, it can be taken too far, and obviously limits the things that you can play to things that you can reach in this manner. (During my student years, I worked out some pretty tortuous fingerings to some of Bach's fugues with this ideal in mind, with decidedly mixed results.) Also, as tempos get faster, legato becomes less of a goal.
For an advanced example of the fingering I'm suggesting, have a look at this, from the last movement of Beethoven's Sonata Op. 31 No. 3 (look at measure 239, right after the trill in the right hand):
This is to be played quite quickly (the tempo marking is presto con fuoco). You can see that the suggested fingering at measure 239 is 532123. You'll also notice that the fingering at measure 243 has the same suggestion, despite the leap of an entire octave. I can tell you from personal experience that I tried (starting at measure 238) 532121 513231 first, and wasn't able to get it up to tempo. So, I took the "leap of faith" (well, my teacher told me to, so I did it) and learned how to hit that Db octave using 353. Once I had the distance down, it went a lot smoother.
Now, here is Daniel Barenboim playing the passage, and it's not too hard to see that he uses exactly this fingering (and makes it look very easy, of course, which it isn't).
Finally, lest you get the idea that such fingerings are reserved for people with Barenboim-sized hands, here's a young lady clearly using the same fingering. In fact, if you go on a bit, you'll notice that she doesn't pass thumb under finger (or finger over thumb) at all in the entire passage:
So, you'll want to learn how to do this. Your example piece is a good one to get started developing a good legato broken chord technique, connecting notes through proper use of the pedal.
Since the next set of arpeggios is basically a mirror of the previous set, I would suggest moving your hand down, and using the same fingering if you are comfortable with it.
As in: 5 2 1 2 1 2 shift 5 2 1 2 1 2
As Kilian Foth states, the arpeggio is the same spacing as the Ab one earlier in the bar. If that fingering works, then the same fingering will work for the Eb arp. in the second half. Because they are arps, the sustain pedal will help the lower note, and also make the part sound better.
However, I'd spread my hand to play 5-3-2-1-2-3.
I have a big hand, so I wouldn’t cross the thumb at all. Chopin is another good source for pedaling ideas. And he often didn’t follow “the rules” regarding fingering and pedaling.
