Structural isomer population of a hydrogen bonded cluster generally depends on temperature. Therefore, determination of an isomer population profile in a wide temperature range is important to understand the nature of hydrogen bond networks of the cluster. To explore an isomer population profile, stepwise changes of internal vibrational energy of a protonated hydrogen-bonded cluster are performed by inert gas tagging. We observe infrared spectra of the protonated methanol pentamer with various tag species. The bare protonated methanol pentamer practically has only two possible isomer types. With the tagging, the relative population of the two isomer types changes according to the binding energy with the tag species. The observed relative population follows its theoretically predicted temperature dependence.