  We present predictions for the equation of state of symmetric nuclear and
pure neutron matter based on recent high-quality nucleon-nucleon potentials
from leading order to fifth order in the chiral expansion. We include as well
the next-to-next-to-leading order (N2LO) chiral three-nucleon force whose
low-energy constants cD and cE are fitted to the binding energies of 3H and 3He
as well as the \b{eta}-decay lifetime of 3H. The ground state energy per
particle is computed in the particle- particle ladder approximation up to a few
times saturation density. Due to the soft character of the interactions,
uncertainties due to the convergence in many-body perturbation theory are
small. We find that nuclear matter saturation is reproduced quantitatively at
N3LO and N4LO, and therefore we encourage the application of these interactions
in finite nuclei, where the description of ground- state energies and charge
radii of medium-mass nuclei may be improved.
