The 5th finger is not actually weak. In fact despite its size it is rather strong, and has additional muscles that the other fingers lack. The problem is in the brain. You have to build up neural pathways to make it (the 5th finger - and also the 4th finger) move with the same sort of speed and precision as thumb, 2, 3.
A good exercise is chromatic minor 3rds:
Fingered (RH ascending starting on C-Eb) 13-24-15-24-15-13-24-13-24-15-24-15-13 on the way up
Reverse this on the way down.
You can figure out the LH as the mirror image (Start on C#-E descending with the above fingering).
This is also good practice for a difficult bit in Chopin Op28 No 24.