  Let M be a CR manifold of hypersurface type, which is Levi degenerate but
also satisfying a k-nondegeneracy condition at all points. This might be only
if dim M is greater than or equal to 5 and if dim M = 5, then k= 2 at all
points. We prove that for any 5-dimensional, uniformly 2-nondegenerate CR
manifold M there exists a canonical Cartan connection, modelled on a suitable
projective completion of the tube over the future light cone {z\in C^3:
(x^1)^2+(x^2)^2-(x^3)^2 = 0, x^3>0}. This determines a complete solution to the
equivalence problem for this class of CR manifolds.
