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Ag$_5$Pb$_2$O$_6$ has attracted considerable attention due to its novelnearly-free-electron superconductivity, but its electronic structure andorbital character of the Cooper-pair electrons remain controversial. Here, wepresent a method utilizing core-level photoemission to show that Pb 6$s$electrons dominate near the Fermi level. We observe a strongly asymmetric Pb4$f_{7/2}$ core-level spectrum, while a Ag 3$d_{5/2}$ spectrum is wellexplained by two symmetric peaks. The asymmetry in the Pb 4$f_{7/2}$ spectrumoriginates from the local attractive interaction between conducting Pb 6$s$electrons and a Pb 4$f_{7/2}$ core hole, which implies a dominant Pb 6$s$contribution to the metallic conduction. In addition, the observed Pb4$f_{7/2}$ spectrum is not explained by the well-known Doniach-\v{S}unji\'{c}lineshape for a simple metal. The spectrum is successfully generated byemploying a Pb 6$s$ partial density of states from local density approximationcalculations, thus confirming the Pb 6$s$ dominant character andfree-electron-like density of states of Ag$_5$Pb$_2$O$_6$.

Element-Specific Orbital Character in a Nearly-Free-Electron Superconductor Ag$_5$Pb$_2$O$_6$ Revealed by Core-Level Photoemission