Ag5Pb2O6 has attracted attentions due to its novel nearly-free-electron superconductivity, but its electronic structure and orbital character of the Cooper-pair electrons remain controversial. Here, we present a method utilizing core-level photoemission to show that Pb 6s electrons dominate near the Fermi level. We observe a strongly asymmetric Pb 4 f 7/2 core-level spectrum, while a Ag 3d 5/2 spectrum is well explained by two symmetric peaks. The asymmetry in the Pb 4 f 7/2 spectrum originates from the local attractive interaction between conducting Pb 6s electrons and a Pb 4 f 7/2 core hole, which implies a dominant Pb 6s contribution to the metallic conduction. In addition, the observed Pb 4 f 7/2 spectrum is not explained by the well-known Doniach-Šunjić lineshape for a simple metal. The spectrum is successfully generated by employing a Pb 6s partial density of states from local density approximation calculations, thus confirming the Pb 6s dominant character and free-electron-like density of states of Ag5Pb2O6.