The Melodic Style of playing the 5 string banjo is a type of banjo playing that was popularized by Bill Keith. This style allows the banjoist to play scales and fiddle tunes in a finger efficient way by never repeating 2 sequential notes on the same string. In this style you can play the complete melody of fiddle tunes, something that you cannot do when using the Scruggs style.
Listen and watch Tray Wellington cover the basics of Melodic Style banjo with his Deering Tenbrooks Saratoga Star banjo.