We report on the systematic observation of emission spectra of (RbHen)-He-* exciplexes (n=1,2,...,6), realized by exciting Rb atoms to the 5(2)P states (Rb-*) in a cold He-4 gas. The observed broad spectral components are assigned to (RbHen)-He-* (n=1-6) using theoretical spectra obtained from ab initio potential curves. The dynamics of the exciplex formation is discussed, based on the observed temperature dependence of the spectra. The He gas density dependence of the spectra of (RbHe)-He-* is understood as a change in the population distribution over the vibrational levels. The present results are compared with our previous work with Cs [K. Enomoto , Phys. Rev. A 66, 042505 (2002)], and differences are explained in terms of the difference in the fine-structure splitting. Furthermore, we show the emission spectrum observed after the excitation of Rb in liquid He and conclude that it is the fluorescence from the exciplex (RbHe6)-He-*.