The invention relates to a novel cephalosporin compound with a general formula (I), pharmaceutically acceptable salt(s) thereof, easy hydrolysable ester(s) thereof, isomer(s) thereof, hydrate(s) thereof, and hydrate(s) of the salt(s) or ester(s) thereof, wherein, R <1>, R<2>, R<3>, R<4>, R<5> and X are defined in the specification. The invention also relates to preparation methods of these compounds, the medicine compositions containing these compounds, and applications of these compounds in preparing medicines for treatment and / or prevention of infective diseases, pertaining to medicine technique field.