  We give in this paper which is the fifth in a series of eight a theory of
covariant derivatives of multivector and extensor fields based on the geometric
calculus of an arbitrary smooth manifold M, and the notion of a connection
extensor field defining a parallelism structure on M. Also we give a novel and
intrinsic presentation (i.e., one that does not depend on a chosen orthonormal
moving frame) of the torsion and curvature fields of Cartan's theory. Two kinds
of Cartan's connection fields are identified, and both appear in the intrinsic
Cartan's structure equations satisfied by the Cartan's torsion and curvature
extensor fields.
