If you play hard rock, metal, alternative, or anything related to power chords, the Minor Pentatonic Scale can be a good buddy of yours. For example, say you're jamming along with someone who is playing a progression of Power Chords that begins from the 6th string, 5th fret. Power chords are neither major nor minor chords--as they contain a root, 5th, but no third. Anyhow, we're going to treat this power chord as a minor. The power chord starts on the 6th string, 5th fret and so will your pentatonic shape.
I would suggest that you go ahead and learn 6th string tonics of each shape. First, learn to mobilize this shape, then move onto other shapes that seem easy to apply from the 6th string.