Dielectron $p_{\rm T,ee}$-differential yields in peripheral (70--90\%) Pb--Pb collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV for three different $m_{\rm ee}$ ranges, i.e. $0.4 \leq m_{\rm ee} < 0.7$ GeV/$c^2$ (left), $0.7 \leq m_{\rm ee} < 1.1$ GeV/$c^2$ (middle), and $1.1 \leq m_{\rm ee} < 2.7$ GeV/$c^2$ (right), compared with the expected e$^+$e$^-$ contributions from known hadronic decays and calculations for coherent two-photon production of dielectrons folded with the detector resolution. For details see the text. The error bars and boxes represent the statistical and systematic uncertainties of the data, respectively, whereas the bands show the uncertainties of the hadronic cocktail. Arrows indicate upper limits at 90\% confidence level.