  On a real analytic 5-dimensional CR-generic submanifold M^5 in C^4 of
codimension 3, hence of CR dimension 1, which enjoys the generically satisfied
nondegeneracy condition that Lie brackets up to length 3 of T^{1,0}M generate
CTM, a canonical Cartan connection is constructed after reduction to a certain
partially explicit e-structure of the concerned local biholomorphic equivalence
problem. More advanced explorations of the incoming differential invariants due
to the first and to the third authors already appeared in January 2014, hence
the purpose is to show, while studying this specific Class III-1 of
5-dimensional CR structures, why and how the construction of Cartan geometries
usually provides less information than a complete ramified discussion of
potentially normalizable essential torsion coefficients.
