The excitation of multiple surface-plasmon-polariton (SPP) waves by the plane wave illumination of a metallic surface-relief grating coated with a sculptured nematic thin film (SNTF) was studied theoretically. The relevant boundary-value problem was formulated such that the grating plane and the morphologically significant plane of the SNTF can be rotated about a common axis with respect to each other. The rigorous coupled-wave analysis was employed to numerically solve the boundary-value problem. Absorptances were calculated as functions of the angle of incidence of a linearly polarized plane wave with wave vector lying wholly in the grating plane, and the excitation of the SPP waves was inferred from those peaks in the absorptance curves that were independent of the thickness of the SNTF. These peaks were successfully correlated with the solutions of the underlying canonical problem solved in Part IV of this series of papers.