In an electron-ion recombination study with Pb53+ dielectronic recombination resonances are found for as low as similar to 10(-3)-10(-4) eV relative energy. The resonances have been calculated by relativistic many-body perturbation theory and through comparison with experiment the Pb53+(4p(1/2)-4s(1/2)) energy splitting of similar to 118 eV is determined with an accuracy comparable to the position of the first few resonances, i.e., similar to 10(-3) eV. Such a precision provides a test of QED in a many-body environment at a level which can still not be reached in calculations.