[en] Anomalously enhanced nonlinear electromagnetic coupling can arise from ordered driven collective motions in many electron systems. The augmented strength of the interaction can be expressed as an effective increase in the fine structure constant α in which α  → Z²α, where Z specifies the number of electrons involved in the ordered response to the external field. The present work illustrates this phenomenon in the x-ray range with the observation of the 5-photon nonlinear excitation of Xe(L)* hollow atom states that are generated by intense (∼7 × 10¹⁵ W cm⁻²) Xe(M) radiation ${\mathrm{\gamma <!--\; ??\; -->}}_{\mathrm{M}}$ at ∼1 keV. The nonlinear cross section experimentally determined for the $5{\mathrm{\gamma <!--\; ??\; -->}}_{\mathrm{M}}$ + Xe → [Xe^q+(L)]* + qe⁻ amplitude is ${\mathrm{\sigma <!--\; ??\; -->}}_5$ ∼ 2 × 10⁻²¹ cm². The matching theoretical cross section corresponds to Z = 18, an outcome indicating the participation of the full Xe(4d¹⁰5s²5p⁶) supershell, a dynamic feature of Xe that also plays a significant role in the linear photoionization of neutral Xe atoms in the kilovolt region. For the high-intensity 5γ nonlinear coupling, the outcome for the Xe(L)* hollow atom excitation is an enhancement of the strength of the interaction by a factor of ∼10¹² and, with Z²α > 1, a fundamentally new region of strong coupling is entered. The experimental value of ${\mathrm{\sigma <!--\; ??\; -->}}_5$ is likewise shown to be in very good accord with an earlier analysis that estimated the upper bound of cross sections for high-order multi-photon cross sections in the combined high-Z and high-intensity limit. These results forecast the general presence of comparably enhanced coupling strengths in the interaction of sufficiently intense (I ≥ 7 × 10¹⁵ W cm⁻²) x-rays with high-Z atoms and molecules. (paper)