There is a unique (compatible, second-order) 5D-equation of Absolute Parallelism (D is fixed) which solutions avoid singularities. Three of fifteen polarization modes are linearly unstable; they can carry digital information, topological charges and quasi-charges, but not the five-momentum. Phenomenological models accounting for these (quasi)charges (i.e., particles) emerge including a relativistically expanding S^3-shell cosmology and Lagrangian forth-order gravity. A radial longitudinal wave can form a shell of huge size L (in the co-moving system) along the extra-dimension. The correction to the Newton's law here behaves as 1/r on large scales, r>L, so the Dark Matter hypothesis looks unnecessary. Generation of gravitational waves (GW) in this theory differs by the factor (\lambda/L)^2 from the General Relativity result (for GW amplitude; \lambda is GW wavelength); so, short GWs should be much weaker than in GR. A new way of interpretation of Quantum Mechanics (closely relating to the huge and "undeveloped" extra-dimension) is briefly discussed.