  The quintet of Dirac $4\times 4$ matrices suggests that the fundamental
dimension of the internal (spin) space is $n=5$, instead of the conventional
dimension $n=4$. Then extending the usual $4\times 4$ tetrads (vierbein),
gravity is described in terms of the 5-bein (f\"unfbein or five legs). We
discuss the properties of the spacetime geometry induced from this 5-leg Dirac
spinor theory, where the spin connection contains $10\times 4=40$ elements
instead of 24 elements in the tetrad formulation of the general relativity
theory.
