Dielectronic recombination of Pb53+ has been studied and a resonance is detected only similar to 10(-4) eV above the ground state. The possibility to determine the Pb53+ (4p(1/2)) - Ph53+ (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 quantum electrodynamics (QED) in a many-body environment at a level which can still not be reached. A fully relativistic many-body calculation of the splitting is described and the uncertainties are discussed.