Music appreciation: in beethoven's  fifth symphony,  the third movement moves through several different keys as it approaches the triumphant c major of the fourth movement. this movement through keys is known as                a.  modulation.      b.  recapitulation.      c.  sonata form.      d.  tonality.

This movement through keys is known as A. modulation.
Modulation refers to the changing of one key, which can be tonic or tonal center, onto another, which fits your description. Recapitulation refers to sections of movements within a sonata; Fifth Symphony is a symphony, not a sonata form; tonality refers to pitches and chords, not keys.