First, I agree with alephzero about the fingering. The fingering in your edition assumes that you start on the upper auxiliary rather than the lower, and as I have detailed in my note to his answer this is not set in blood. If you like the lower auxilary, then reverse the numbers in the fingerings. 4-2 on the lower notes and 5-1 on the uppers, changing to 3-2 on the lowers when the Cx moves to C#.
Now, you can go to Hanon or Czerny (or Chopin's G# minor etude if you really want a serious challenge) and look for trill exercises, but this is a great one in its own right. You can treat it like its own strengthening exercise.
I'll amplify what alephzero said about "extra credit". To start with, play the passage as if it were a fairly slow melody. Forget about playing it fast, forget about teaching yourself how to play a trill, just focus on the (actually more difficult) challenge of making music out of that trill passage when you are playing it slowly enough for all the notes to be distinct. You'll definitely notice some weakness in 4 and 5, but you'll probably notice even more the lack of coordination between the two fingers. Work to balance the placement of the fingers on the keyboard so they can play the notes smoothly. And above all, forget that it is more difficult to play a trill with 4-5 than it is with 2-3. You're not playing a trill right now, you're playing a melody. As you get that sense of melody, you'll find it begins to take off. The longer you can hold onto the sense of making music first and a trill second, the better you will execute the trill once you work up to it.