We have measured the absolute frequency of the excited state transition $5P_{3∕2}–4D_{5∕2}$ in a ${}^{87}\mathrm{Rb}$ atom with a femtosecond frequency comb, utilizing the recently developed spectroscopic technique of the double resonance optical pumping method. The absolute energy level of the $4D_{5∕2}$ state is determined by measuring the absolute frequency of the $5S_{1∕2}–5P_{3∕2}$ transition simultaneously. The hyperfine structure constants of the $4D_{5∕2}$ state are obtained by using the measured frequency. The magnetic dipole constant, A, is determined to be $(-16.747\pm 0.010)\mathrm{MHz}$ with an uncertainty reduced 60-fold compared with a previous result. The electric quadrupole constant, B, is determined, for what is to our knowledge the first time, to be $(4.149\pm 0.059)\mathrm{MHz}$ .