Polycrystalline samples of Sr0.5RE0.5FBiS2 (RE: La, Ce, Pr, Nd, and Sm) were synthesized via the solid-state reaction and characterized using synchrotron X-ray diffraction. Although all the Sr0.5RE0.5FBiS2 samples exhibited superconductivity at transition temperatures (Tc) within the range of 2.1-2.7 K under ambient pressure, the estimated superconducting volume fraction was small, which indicates non-bulk nature of superconductivity in those samples under ambient pressure. A dramatic increase in shielding fraction, which indicates the emergence of the bulk superconductivity was achieved by applying external hydrostatic pressures. We found that two phases, low-P phases with Tc = 2.5-2.8 K and high-P phases with Tc = 10.0-10.8 K, were induced by the pressure effect for samples with RE = La, Ce, Pr, and Nd. Pressure-Tc phase diagrams indicated that the critical pressure for the emergence of the high-P phase tends to increase with decreasing ionic radius of the doped RE ions, which was explained by the correlation between external and chemical pressure effects. According to the high-pressure X-ray diffraction measurements of Sr0.5La0.5FBiS2, a structural phase transition from tetragonal to monoclinic also occurred at approximately 1.1 GPa. Bulk superconducting phases in Sr0.5RE0.5FBiS2 induced by the external hydrostatic pressure effect are expected to be useful for understanding the effects of both external and chemical pressures to the emergence of bulk superconductivity and pairing mechanisms in BiCh2-based superconductors.