The differential invariant yield as a function of transverse momentum (p_T) of electrons from semileptonic heavy-flavour hadron decays was measured at midrapidity in central (0–10%), semi-central (30–50%) and peripheral (60–80%) lead–lead (Pb–Pb) collisions at s_NN=5.02 TeV in the p_T intervals 0.5–26 GeV/c (0–10% and 30–50%) and 0.5–10 GeV/c (60–80%). The production cross section in proton–proton (pp) collisions at s=5.02 TeV was measured as well in 0.5<p_T<10 GeV/c and it lies close to the upper band of perturbative QCD calculation uncertainties up to p_T=5 GeV/c and close to the mean value for larger p_T. The modification of the electron yield with respect to what is expected for an incoherent superposition of nucleon–nucleon collisions is evaluated by measuring the nuclear modification factor R_AA. The measurement of the R_AA in different centrality classes allows in-medium energy loss of charm and beauty quarks to be investigated. The R_AA shows a suppression with respect to unity at intermediate p_T, which increases while moving towards more central collisions. Moreover, the measured R_AA is sensitive to the modification of the parton distribution functions (PDF) in nuclei, like nuclear shadowing, which causes a suppression of the heavy-quark production at low p_T in heavy-ion collisions at LHC.