In a lead sheet, the melody is notated with the chord symbols indicated above the staff. Play this melody with the right hand and "realize" the written chord symbol by playing the named note, called the root tone, on the downbeat with the left hand. (MM. 1-4 are shown as an example.) Notice that your hands are not covering the same 5-finger position.
L.H. on D minor 5-finger position - R.H. on A minor 5-finger position