In general, a single-resonator absorber can exhibit only a single absorption band under fundamental mode resonance while a multiband absorber can be achieved by combining resonators of different sizes. However, because of disturbances between adjacent resonators, it is difficult to obtain a multiband absorber containing more than four absorption bands within a certain frequency range in which all absorption peaks simultaneously exhibit an absorptivity greater than 90%. In this work, based on a metal/insulator/metal structure, we design a single complex resonator absorber to provide five absorption bands with absorptivities greater than 90%. A large-perimeter metallic structure combined with small strips is the key factor of this design. The former allows the excitation of high-order mode resonances, whereas the latter provide high absorptivity. Our investigations could not only extend the design ideas for multiband absorbers but also offer useful design clues for devices based on multimode resonances.