Share 'Buzz on the A string between 5th and 7th fret'

Customer wanted action lowered on a Martin D-35.  Guitar had plenty of saddle to adjust.  I checked the relief was between .010 and .016.  Nut is in good shape.  The action before was approximately 3mm on bass, 2mm on treble at 12th fret, but customer wanted a little lower.  After lowering to 2.7mm on bass and 1.5 on treble, guitar played very well except A string at 5th and 7th fret.  I checked…