We combined high resolution Fourier-transform spectroscopy and large scale electronic structure calculation to study energy and radiative properties of the high-lying (3) 1 Π and (5) 1 Σ + states of the RbCs molecule. The laser induced (5) 1 Σ + ,(4) 1 Σ + ,(3) 1 Π →A(2) 1 Σ + ∼ b(1) 3 Π fluorescence (LIF) spectra were recorded by the Bruker IFS-125(HR) spectrometer in the frequency range ν ∈ [5500, 10000] cm −1 with the instrumental resolution of 0.03 cm −1 . The rotational assignment of the observed LIF progressions, which exhibit irregular vibrational -rotational spacing due to strong spin-orbit interaction between A 1 Σ + and b 3 Π states was based on the coincidences between observed and calculated energy differences. The required rovibronic term values of the strongly perturbed A∼b complex have been calculated by coupled -channel approach for both 85 Rb 133 Cs and 87 Rb 133 Cs isotopolgues with accuracy of about 0.01 cm −1 , as demonstrated in [A. Kruzins et. al., J. Chem. Phys. 141,184309 (2014)]. The experimental energies of the upper (3) 1 Π and (5) 1 Σ + states were involved in a direct-potential-fit analysis performed in the framework of inverted perturbation approach. Quasi-relativistic ab initio calculations of the spin-allowed (3) 1 Π,(5) 1 Σ + → (1-4) 1 Σ + ,(1-3) 1 Π transition dipole moments were performed. Radiative lifetimes and vibronic branching ratios of radiative transitions from (3) 1 Π and (5) 1 Σ + states were evaluated. To elucidate the origin of the Λ-doubling effect in the (3) 1 Π state the angular coupling (3) 1 Π-(1-5) 1 Σ + electronic matrix elements were calculated and applied for the relevant q−factors estimate. The intensity distributions simulated for the particular (5) 1 Σ + ;(3) 1 Π →A∼b LIF progressions have been found to be remarkably close to their experimental counterparts.