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High-entropy-alloy (HEA) superconductors are a new class of disordered superconductors. In this study, we investigate the robustness of superconducting states in HEA-type metal telluride (MTe; M = Ag, In, Sn, Pb, Bi) under high pressure. PbTe exhibits a structural transition from a NaCl-type to an orthorhombic Pnma structure at low pressures, and further transitions to a CsCl-type structure at high pressures. When the superconductivity of the CsCl-type PbTe is observed, it is found that its superconducting transition temperature (Tc) decreases with pressure. However, in the HEA-type AgInSnPbBiTe5, Tc is almost independent of pressure, for pressures ranging from 13.0 to 35.1 GPa. This trend is quite similar to that observed in an HEA superconductor (TaNb)0.67(HfZrTi)0.33, which shows that the robustness of superconductivity to external pressure is a universal feature in HEA-type superconductors. To clarify the effects of the modification of the configurational entropy of mixing on the crystal structure, superconducting states, and electronic structure of MTe, electrical resistance measurements, synchrotron X-ray diffraction, and synchrotron X-ray absorption spectroscopy with partial fluorescence mode (PFY-XAS) for three MTe polycrystalline samples of PbTe, AgPbBiTe3, and AgInSnPbBiTe5 with different configurational entropies of mixing at the M site were performed.