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Joule-Thomson cryo-refrigerators operating on mixed working fluids have significant advantages over chillers using pure refrigerants. When optimizing the composition of zeotropic refrigerant mixtures, it is necessary to take into account the peculiarities of the operation of volumetric compressors. It is known that the flow rate of a reciprocating compressor significantly depends on the compression ratio and the compressor suction pressure. Therefore, it is impractical to optimize the composition of zeotropic refrigerant mixtures at a fixed molar flow rate, as is done in many studies. This paper describes a method for optimizing the operation of a refrigeration machine operating on a five-component zeotropic mixture of refrigerants. The maximum cooling capacity of the unit at the temperature of 120 K, which is based on a hermetic compressor TAG 2513Z, was chosen as the objective function. The following parameters were varied during the optimization: compressor discharge and suction pressures, the composition of the five-component working mixture, as well as the temperature upstream of the throttle valve, and the temperature at the inlet to the phase separator. As a result of processing the results of the numerical experiment, an analytical expression was obtained that approximates the operation of the refrigeration unit depending on the eight varied parameters. This made it possible to find the optimal operating mode of the refrigeration machine, which achieves maximum cooling capacity. At the optimum operating mode of the refrigeration unit, the suction pressure is 2.35 bars, and the discharge pressure is 16.0 bars. With the optimal composition of the working substance, the maximum cooling capacity of 147.7 W with energy consumption by the compressor of 2.36 kW is achieved. [ABSTRACT FROM AUTHOR]