Dielectronic recombination of Pb53+ has been studied and a resonance is detected only similar to 0.1 meV above the ground state. The possibility to determine the 4p(1/2) - 4s(1/2) energy splitting with a similar accuracy from the determination of the resonance position is discussed. Such a precision can only be achieved by calculations which treat QED in a many-body environment at levels which can still not be reached. A fully relativistic many-body calculation of the splitting is described and the uncertainties are discussed.