The frequency of C5, one octave above middle C, is 523.25 Hz in twelve-tone equal temperament.
This value is calculated from the standard tuning reference A4 = 440 Hz. In equal temperament, an octave is divided into twelve equal semitones, each with a frequency ratio of the twelfth root of two. C5 lies nine semitones above A4, so its frequency is approximately 523.251 Hz, conventionally rounded to 523.25 Hz.
The note is called C5 in scientific pitch notation, where the number identifies the octave. Middle C is C4, not C5, and has a frequency of about 261.63 Hz under the same tuning system. That octave relationship explains why C5 is exactly twice the frequency of C4.
The 523.25 Hz figure assumes equal temperament and the modern A4 reference of 440 Hz. Other tuning systems or reference pitches can produce slightly different values. For comparison, 440 Hz is A4, while 1046.5 Hz is C6, two octaves above middle C.