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We use the Percus-Yevick approach in the chemical-potential route to evaluatethe equation of state of hard hyperspheres in five dimensions. The evaluationrequires the derivation of an analytical expression for the contact value ofthe pair distribution function between particles of the bulk fluid and a soluteparticle with arbitrary size. The equation of state is compared with thoseobtained from the conventional virial and compressibility thermodynamic routesand the associated virial coefficients are computed. The pressure calculatedfrom all routes is exact up to third density order, but it deviates withrespect to simulation data as density increases, the compressibility and thechemical-potential routes exhibiting smaller deviations than the virial route.Accurate linear interpolations between the compressibility route and either thechemical-potential route or the virial one are constructed.

Equation of state for five-dimensional hyperspheres from the chemical-potential route