Quantum-electrodynamical corrections to energy levels of helium are calculated with an accuracy of α5mc2 on the basis of the Bethe-Salpeter equation according to the perturbation method of Fulton and Karplus. The interaction kernel of the equation is derived according to the method of Martin and Schwinger. The corrections are carefully calculated by the method which is free from any doubt. The result is expressed in terms of non-relativistic eigenfunctions. It is found for α5mc2 corrections that correction factors for spin-orbit and spin-spin couplings are in complete agreement with those derived by G. Araki on the basis of a simple consideration. Since α4mc2 corrections often gave rise to confusions and discussions among many authors these corrections are carefully examined. It is found on the firm basis that the α4mc2 terms involve a contact interaction but not the Breit surplus term. Further it is found that the energy correction for the excited bound state includes an imaginary part. Of course the ground-state energy is real. In fact the absolute value of the imaginary part represents half the width of the level in question. A discussion for this fact is given.