As for the fingering, I use 4 instead of 5 there, and probably most people would. A reason not to is that it might be quicker to get 3 on A if 5 is on F# than if 4 is. Since the passage is pretty rapid, and also pedaled, it's acceptable to make a small jump between 1 and 5, so that might be the motivation for the fingering. Nevertheless I find 4 easier to use here, and the best finger to get a smooth passage.
Also, though, that looks like a Schirmer edition, and some of the Victorian fingerings in those editions are hopelessly pedantic. Meaning, fingerings often appear to be chosen because of what was considered "proper technique" in that time period rather than what works best. Hanon had a finger exercise (number 35) designed to practice little finger over thumb and thumb under little finger, and put a little note "this exercise is of the highest importance." Well, no it isn't. The only place I can think of that really requires it is the run near the end of Chopin's Prelude No. 24 in D minor:
Admittedly, I don't play that passage well, so perhaps the exercise is more important than I think.