In this paper, in the two-parameter five-dimensional(5D) rotating black hole, we discuss the thermodynamic parameters corresponding to the black hole's horizon and the thermodynamic parameters corresponding to the cosmological horizon. It is obtained that the entropy of cosmological horizon can be written in the form of Cardy-Verlinde formula. However, if we want to write the entropy of the bla ck hole's horizon in the form of Cardy-Verlinde formula, we have to use the met hods offered by Abbott and Deser to calculate the mass of the 5D black hole with double- spinning parameter. Through the research, we can give the relation among the thermodynamic parameters of the 5D black hole, that is, the differential ex pression of the first law of thermodynamics.
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