  We calculate radiative corrections to the Lamb shift of order
$\alpha^3(Z\alpha)^5m$ and radiative corrections to hyperfine splitting of
order $\alpha^3(Z\alpha)E_F$ generated by the diagrams with insertions of
radiative photons and electron polarization loops in the graphs with two
external photons. We also obtain the radiative-recoil correction to hyperfine
splitting in muonium generated by the diagrams with the $\tau$ polarization
loop.
