Calculations have been performed on 10 structures of the cluster H+(H2O)(5). It is shown that the most stable ones are an open (Eigen) and a cyclic four-membered-ring structure very close in energy and possibly degenerate. This can explain that different structures were proposed by experimentalists. The easy evolution of some structures into others is likely related to the nature of the first solvation shell in larger clusters or solutions. Vibrational frequencies, useful to interpret experimental data, are computed for the two most stable structures.