Hi Max, I’ve had a look at the music. If I was playing this, I’d use 5 fingers. I’ve written the finger numbers in red above the notes. Where there is a number in brackets, it means that you change the finger while holding the key down. This way you can get completely smooth legato with all notes.
To do this, I keep the 3rd finger bent, and play with the back of the finger/nail side.
I hope this helps!