The present work studies the inverse scattering transformation (IST) of the inhomogeneous fifth-order defocusing nonlinear Schrodinger (ifoNLS) equation with zero boundary conditions (ZBCs) and non-zero boundary conditions (NZBCs). Firstly, the bound-state (BS) solitons of the ifoNLS equation with ZBCs are derived by generalization of the residue theorem and the Laurent’s series for the first time. Then combining with the robust IST, the matrix Riemann-Hilbert (RH) problem of the ifoNLS equation with NZBCs are revealed. Based on the resulting RH problem, a new higher-order rogue wave (RW) solution of the ifoNLS equation are found by the modified Darboux transformation. Finally, some corresponding graphs are given by selecting appropriate parameters to further discuss the unreported dynamic behavior of the BS solitons and RW solutions, which have not been reported before.