The strong decays of the 5 1 S 0 qq states are evaluated in the 3 P 0 model with two types of space wave functions. Comparing the model expectations with the experimental data for the π(2360), η(2320), X (2370), and X (2500), we suggest that the π(2360), η(2320), and X (2500) can be assigned as the members of the 5 1 S 0 meson nonet, while the 5 1 S 0 assignment for the X (2370) is not favored by its width. The 5 1 S 0 kaon is predicted to have a mass of about 2418 MeV and a width of about 163 or 225 MeV.