The character table of the fully nonrigid water pentamer, (H2O)(5), is derived for the first time. The group of all feasible permutations is the wreath product group S-5[S-2] and it consists of 3840 operations divided into 36 conjugacy classes and irreducible representations. We have shown that the full character table can be constructed using elegant matrix type generator algebra. The character table has been applied to the water pentamer by obtaining the nuclear spin statistical weights of the rovibronic levels and tunneling splittings of the fully nonrigid pentamer. We have also obtained the statistical weights and tunneling splittings of a semirigid deuterated pentamer that exhibits pseudorotation with an averaged C-5h (G(10)) symmetry used in the assignment of vibration-rotation-tunneling spectra. It is also shown that the previously considered group G(320) for water pentamer of feasible permutations is a subgroup of the full group and is the direct product of wreath product C-5[S-2] and the inversion group. The correlation tables have been constructed for the semirigid (G(10)) to nonrigid (G(3840)) groups for the rotational levels and tunneling levels. The nuclear spin statistical weights have also been derived for both the limits and through the use of subduced representations the corresponding information can be obtained for G(320) as well from G(3840).