Elastic scattering angular distributions of $^{13}$C at 340 MeV and of $^{14}$C at 294 MeV and 342 MeV on a $^{208}$Pb target, which correspond to around five times the Coulomb barriers, were measured at the Radioactive Ion Beam Line in Lanzhou. The data were analyzed within the optical model and the continuum-discretized coupled-channels (CDCC) framework and the results of both calculations can account well for the experimental data. The differential cross sections of elastic scattering show no particular suppression at the Coulomb nuclear interference peak angles, suggesting that the breakup coupling effects to the elastic scattering angular distributions are negligibly small at this incident energy region. The contributions from the couplings with the inelastic states to the elastic cross sections are of minor importance within the angular range covered by present experiments.