  We study dilepton, proton-antiproton and diphoton production in
ultraperipheral lead-lead collisions at $\sqrt{s_{\mathrm{NN}}}$ = 5.02 and 5.5
TeV. The nuclear calculations are based on equivalent photon approximation in
the impact parameter space. For correct description of the $\gamma\gamma \to
p\bar{p} $ Belle data we include the proton-exchange, the $f_2(1270)$ and
$f_2(1950)$ s-channel exchanges, as well as the handbag mechanism. For four
muon production, we take into account electromagnetic (two-photon)
double-scattering production and direct $\gamma\gamma$ production of four muons
in one scattering. The cross sections for elementary $\gamma\gamma \to
\gamma\gamma$ subprocess are calculated including three different mechanisms:
box diagrams with leptons and quarks in the loops, a VDM-Regge contribution
with virtual intermediate hadronic excitations of the photons and the two-gluon
exchange contribution. We find that the cross section for elastic
$\gamma\gamma$ scattering could be measured in the lead-lead collisions for the
diphoton invariant mass up to $W_{\gamma\gamma} \approx$ 15 - 20 GeV. Our
Standard Model predictions are compared with a recent ATLAS experimental
result.
  We discuss results for PbPb$\to$PbPb$\mu^+\mu^-\mu^+\mu^-$,
PbPb$\to$PbPb$e^+e^-e^+e^-$, PbPb$\to$PbPb$p\bar{p}$ and
PbPb$\to$PbPb$\gamma\gamma$ reactions at LHC energy.
