We present analytical expressions for the 31 five-particle phase-space master integrals in massless
QCD as an ε-series with coefficients being multiple zeta values of weight up to 12. In addition,
we provide a computer code for the Monte-Carlo integration in higher dimensions, based on the
RAMBO algorithm, that has been used to numerically cross-check the obtained results in 4, 6,
and 8 dimensions.