there are tricks to getting speed

I had to use one to get the L hand up to snuff for flight of the Bumblebee where the L hand has an ascending chromatic scale and the tempo is presto!
for speed:
play the first note and hold... play the next 4 notes as fast as you can and pause for a time then continue
once you have increased your velocity then try inverting the sequence and play the first 5 notes really fast and hold on the the last note
next play two units without a pause
ie play the first note then play 9 notes fast
you can alsoplay 4 fast 4 slow 4 fast 4 slow
and syncopated rhythyms can help build speed
when playing the 4 notes fast think of the movement that kids use when they play that silly song with their knuckes by rolling across the notes. The velocity comes for the fingers getting trained but also the shoulder moving the hand along the horizontal axis of the keyboard plus the wrist rolling a little also.
I sometimes use the chopin fingerings ( with the 4th finger) but mostly use the 13132 method because it feels more natural to me...
Bob S Reno, NV
Bob S