The possible members of the $5^1S_0$ meson nonet

The strong decays of the \(5^1S_0\) \(q{\bar{q}}\) states are evaluated in the \(^3P_0\) model with two types of space wave functions. Comparing the model expectations with the experimental data for the \(\pi (2360)\), \(\eta (2320)\), X(2370), and X(2500), we suggest that the \(\pi (2360)\), \(\eta (2320)\), and X(2500) can be assigned as the members of the \(5^1S_0\) meson nonet, while the \(5^1S_0\) assignment for the X(2370) is not favored by its width. The \(5^1S_0\) kaon is predicted to have a mass of about 2418 MeV and a width of about 163 or 225 MeV.