The chemical reactions and pathways involving vitamin D5, (1S,3Z)-3-[(2E)-2-[(1R,3aS,7aR)-1-[(1R,4S)-4-ethyl-1,5-dimethylhexyl]-7a-methyl-2,3,3a,5,6,7-hexahydro-1H-inden-4-ylidene]ethylidene]-4-methylene-1-cyclohexanol.
Catalysis of the reactions: isocitrate + NAD+ = 2-oxoglutarate + CO2 + NADH, and (1R,2S)-1-hydroxybutane-1,2,4-tricarboxylate + NAD+ = 2-oxoadipate + CO2 + NADH + H+.