The collisional energy transfer process Rb(5PJ)+M, where M= He, N2, under gas cell conditions has been investigated. The Rb(5P3/2) state was excited by a diode laser. The direct 5P3/2-->5S1/2 fluorescence and the sensitized 5P1/2-->5S1/2 fluorescence as a function of quenching gas pressure were measured. The 5P3/2 and 5P1/2 states are separated by 238 cm(-1). The closest other states are >6500 cm(-1) or >28 KT. Neglect of these other states should be an excellent approximation. In the experiment the Rb density was 4.5 x 10(11) cm(-3). Using radiation trapping theory the effective radiative rate=Gammae5P3/2-->5S1/2 2.47 x 10(7) s(-1) was obtained. For quenching by He only electronic to translational energy transfer is possible. However, in the N2 case, electronic to vibrational or rotational transfer is important. The Rb(5P3/2) state is 13 cm(-1) lower than the N2[X'Sigmag+ (V= 5, J= 11)]state; this energy gap is near resonant. The authors have not attempted to directly observe this possible E-R quenching channel Using a two-state rate equation model the transfer rate coefficients from Rb(5PJ) were obtained. The rate coefficient (k21He) for 5P3/2-->5P1/2 transfer in collision with He is 2.61 x 10(-12) cm3 x s(-1). By comparing the direct and sensitized fluorescence intensities for He and N2 case, and fitting the experimental results to the rate equation analysis, the authors estimate that the rate coefficient (k21N2) for 5P3/2-5P1/2 transfer in collision with N2 is 2.36 x 10(-11) cm3 x s(-1). The E-V quenching rate coefficient (kN2) of the 5PJ state is 1.44 x 10(-10) cm3 x s(-1). The authors found find that the rate coefficient kN2 is about 6 times larger than the k21N2. The assumption that the Cs-N2 energy transfer occurs primarily in collinear collision geometry is supported. The results are discussed in relation to those of other experiments.