How do I analyze a music file ( only contains 5 seconds of note A) using the FFT plot to determine the note being played?
An FFT magnitude peak frequency (derived from a single FFT result index) is not reliably the same thing as the music pitch frequency or the musical note.  Note pitch is a psychoacoustic phenomena, and more reliably related to periodicity than the (sinusoidal) spectral peak frequency (e.g. a periodic/repeating waveform shape does not need to look like a sine wave).  See FFT Pitch Detection methods: Autocorrelation or other? for a list of some better methods for estimating note pitch frequency or the musical note.