The exact superconducting phase of K2−xFe4+ySe5 has so far not been conclusively decided since its discovery due to its intrinsic multiphase in early material. In an attempt to resolve this mystery, we have carried out systematic structural studies on a set of well-controlled samples with exact chemical stoichiometry K2−xFe4+xSe5 (x = 0─0.3) that are heat-treated at different temperatures. Using high-resolution synchrotron radiation X-ray diffraction, our investigations have determined the superconducting transition by focusing on the detailed temperature evolution of the crystalline phases. Our results show that superconductivity appears only in those samples that have been treated at high-enough temperature and then quenched to room temperature. The volume fraction of superconducting transition strongly depends on the annealing temperature used. The most striking result is the observation of a clear contrast in crystalline phase between the nonsuperconducting parent compound K2Fe4Se5 and the superconducting K2−xFe4+ySe5 samples. The X-ray diffraction patterned can be well indexed to the phase with I4/m symmetry in all temperatures investigated. However, we need two phases with similar I4/m symmetry but different parameters to best fit the data at a temperature below the Fe vacancy order temperature. The results strongly suggest that superconductivity in K2−xFe4+ySe5 critically depends on the occupation of Fe atoms on the originally empty 4d site.