"If playing in "Am" pentatonic, the first note at the fifth fret is "A" therefore it is a minor scale. When moved down 3 frets the "A" at fret five becomes the second note therefore making it an "A" major scale. Question; The first note of the "A" major scale seems to be an "F"# so isn't this really an "F#" minor pentatonic, or am I not understanding this correctly?"
F minor and A major pentatonic are the same notes, same patterns. The only difference in the two keys is which note is functioning as the root. For example, "Amie" by Pure Prairie League" uses the patterns over an A major chord. So you hear everything revolve around the A note in the scale. This produces a major tonality. The solo to "Over the Hills and Far Away" by Led Zeppelin uses the same patterns but over an F# minor chord. So you hear everything revolve around the F# note in the scale. This produces a minor tonality.Â
By the way, when you're playing over chords it doesn't matter which note you start on. Any note in the key is fair game. I say this so that you won't get hung up on which note you begin playing a pentatonic pattern from. What you're playing over is more important than which note in the pattern you're starting from. I demonstrate this at the end of my pentatonic scale DVD. This musical concept is also explained in Fretboard Theory Chapter 8: Modes.