Evidence for the light-by-light scattering process, γγ → γγ, in ultraperipheral PbPb collisions at a centre-of-mass energy per nucleon pair of 5.02 TeV was reported by the CMS Collaboration at the LHC based on a data sample corresponding to an integrated luminosity of 390 µb−1. Light-by-light scattering processes were selected from the events in which only two photons are exclusively produced, each with transverse energy E_T^γ > 2 GeV, pseudorapidity | η^(γ )| < 2.4, diphoton invariant mass m^γγ > 5 GeV, diphoton transverse momentum p_T^γγ < 1 GeV, and diphoton acoplanarity below A < 0.01. 14 events were observed after all selection criteria, compared to expectations of 9.0 ± 0.9 (theo) events for the signal and 4.0 ± 1.2 (stat) for the background processes. The excess observed in data relative to the background-only expectation corresponds to a significance of 3.7 standard deviations and has properties consistent with those expected for the light-by-light scattering signal. The measured fiducial light-by-light scattering cross section, σ_fid(γγ → γγ) = 120 ± 46 (stat) ± 28 (syst) ± 12 (theo) nb, is consistent with the Standard Model prediction. The m^γγ distribution was used to set constraints on the production of pseudoscalar axion-like particles via the γγ → a → γγ process in the mass range m_a = 5–90 GeV