The C Shape, and the Stretch
The C shape completes the set. Like the D and G shapes it is awkward as a full barre chord, because moving open C intact requires holding a barre with the index finger while stretching the little finger three frets above it.
Its root is on the fifth string, the same as the A shape. Here it is moved up so the root lands on the fifth fret, making a D.
D
D major in the C shape. The root is the fifth-string note at the fifth fret; the rest of the shape sits below it.
And here it is as a full barred version, which is a genuine stretch and which you should treat as optional.
G
G major in the C shape, spanning the seventh to tenth frets. Play the top four strings of this if the full version fights you.
The reason to learn the C shape, even if you rarely play it whole, is the note on top. Every shape puts a different chord tone in the highest voice — the E shape puts the root on top, the A shape the fifth, the C shape the third — and the top note is the one a listener hears most clearly.
That is why two guitarists playing the same chord in different shapes sound like an arrangement rather than a doubling. It is also the practical reason to learn all five rather than stopping at two: not so you can play a G in five places for its own sake, but so you can choose which note of the G is on top.