According to Henle Urtext, it is not his fingering, but I think it is a good one in any case. The key is not to hold the stretch, but simply to rotate from 5 to 4; the fourth finger is used to facilitate rotation between the C-Ab-C-Bb-C, etc, and so the fifth must be played almost sideways on the key.
This Etude is probably the easiest of Opus 10. Using 5-3 enables the same rotation that 5-4 does with considerably less tension for a small hand -- or a large hand.
If Chopin used 5-4, then he had a huge stretch between what had to be very elongated fingers 5 and 4.
In fact, there is a photograph of the modelling of his left hand by J. B. Clesinger (1849), reproduced in the Paderewski Edition, that clearly shows the anatomical feature of his hand. LONG fingers with wide spacing on a broad palm. In fact, PERFECT hands for playing Chopin!
The Paderewski Edition offers 5-4 and 5-3 as fingering options. Using 5-4, in my case, would turn this rather easy piece into an unplayable torture chamber of tension.
5-3. That's the workable choice. If you want a REAL Etude exploiting this LH problem, tackle Chopin's Op. 28, No. 24. I think Chopin confused his Etude for his Prelude and vice versa.