Computer simulations have been performed on binary fluid mixtures of hard hyperspheres in four and five dimensions. The equation of state and the radial distribution function have been obtained for a variety of compositions and size ratios. The simulation results for the excess compressibility factor and the contact values of the cross radial distribution functions in both dimensions are described rather accurately by a recent theoretical proposal for these quantities up to a reduced density where some features arise which are reminiscent of a fluid-solid phase transition. (C) 2001 American Institute of Physics.