The p_T-differential production cross sections of prompt and non-prompt (produced in beauty-hadron decays) D mesons were measured by the ALICE experiment at midrapidity (|y|< 0.5) in proton-proton collisions at s = 5.02 TeV. The data sample used in the analysis corresponds to an integrated luminosity of (19.3 ± 0.4) nb⁻¹. D mesons were reconstructed from their decays D⁰→ K⁻π⁺, D⁺→ K⁻π⁺π⁺, and Ds+→ϕπ+→K−K+π+ and their charge conjugates. Compared to previous measurements in the same rapidity region, the cross sections of prompt D⁺ and Ds+ mesons have an extended p_T coverage and total uncertainties reduced by a factor ranging from 1.05 to 1.6, depending on p_T, allowing for a more precise determination of their p_T-integrated cross sections. The results are well described by perturbative QCD calculations. The fragmentation fraction of heavy quarks to strange mesons divided by the one to non-strange mesons, f_s/(f_u + f_d), is compatible for charm and beauty quarks and with previous measurements at different centre-of-mass energies and collision systems. The b b ¯ production cross section per rapidity unit at midrapidity, estimated from non-prompt D-meson measurements, is dσbb¯/dy||y|<0.5=34.5±2.4(stat)−2.9+4.7(tot.syst) μb. It is compatible with previous measurements at the same centre-of-mass energy and with the cross section pre- dicted by perturbative QCD calculations. [Figure not available: see fulltext.]