A typical example is Hanon's The Virtuoso Pianist in 60 Exercises.
[1] Chopin wrote a number of études (studies) that are widely regarded as musical compositions to train musical ability and dexterity of the fingers, with his Op.10 and Op.25.
Another example of an exercise to develop musical skills may be Für Elise,[2] it has been suggested that it was written as an exercise to practice skills on the piano.
In his chapter on Progressive ideas in nineteenth-century teaching he explains some of Chopin's idea's (see above), there is a mention of five-finger exercises.
[9] As a mnemonic, it is a plan of Christian salvation in the Stone-Campbell Movement, where the five fingers represent "faith, repentance, baptism, remission of sins, gift of the Holy Spirit".