We present results for the calculation of the fully- inclusive five-particle phase-space integrals in the massless QCD. The evaluation method is based on a numerical solution of the difference recurrence relations in space-time dimensionality variable with high precision and reconstruction of the analytical results using PSLQ algorithm. Discussed asymptotics of the phase-space integrals in the limit of infinite space-time dimension and various numerical cross-checks of obtained result.