The medium-spin structure of the nuclei $^{93}\mathrm{Rb}$ and $^{95}\mathrm{Rb}$ is studied following the neutron-induced fission of $^{235}\mathrm{U}$ at the PF1B neutron guide, using the FIFI spectrometer, and at the Lohengrin mass spectrometer of the Institut Laue-Langevin Grenoble. These nuclei, plus $^{91}\mathrm{Rb}$, are also studied following the spontaneous fission of $^{248}\mathrm{Cm}$ and $^{252}\mathrm{Cf}$ sources, using the EUROGAM-II and Gammasphere detector arrays, respectively. A high-spin isomeric state, with a half-life of 111(11) ns, is found in $^{93}\mathrm{Rb}$ at an excitation energy of 4422.4 keV, which most likely corresponds to the fully aligned $[\ensuremath{\pi}({g}_{9/2})\ensuremath{\bigotimes}\ensuremath{\nu}({g}_{7/2}{h}_{11/2})]{}_{{27/2}^{\ensuremath{-}}}$ configuration. An analogous configuration is proposed for the 5297.9-keV level observed in $^{91}\mathrm{Rb}$. A new $E3$ decay branch of the 1133.9-keV isomer in $^{91}\mathrm{Rb}$ is found, for which the rather low transition rate of $B(E3)=3.8(10)$ W.u. is determined. The energy of the isomeric state of $^{95}\mathrm{Rb}$ is now proposed to be at 810.6 keV, with a spin of ($9/{2}^{+}$), and its half-life determined to be ${T}_{1/2}=94(7)$ ns. A cascade of prompt transitions is observed on top of the 810.6-keV isomer in $^{95}\mathrm{Rb}$. The near-yrast structures of $^{91}\mathrm{Rb}$, $^{93}\mathrm{Rb}$, and $^{95}\mathrm{Rb}$ are compared to the results of shell-model calculations, which support the proposed $27/{2}^{\ensuremath{-}}$ interpretation of states in $^{91}\mathrm{Rb}$ and $^{93}\mathrm{Rb}$. An analogous $27/{2}^{\ensuremath{-}}$ state is expected to occur in $^{95}\mathrm{Rb}$, as a long-lived isomer at 3.24 MeV. No such isomeric decay could be observed in a measurement using the Lohengrin spectrometer, which shows that, if it exists, its population, following the fission of $^{235}\mathrm{U}$, is at least four times lower than that of the analogous $27/{2}^{\ensuremath{-}}$ isomer in $^{97}\mathrm{Y}$.