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We continue to explore the bootstrap approach to five-point correlationfunctions for IIB supergravity on $AdS_5\times S^5$. Building on the result of[1], we develop an improved algorithm that allows us to more efficientlycompute correlators of higher Kaluza-Klein modes. The new method uses onlyfactorization and a superconformal twist, and is entirely within Mellin spacewhere the analytic structure of holographic correlators is simpler. Using thismethod, we obtain in a closed form all five-point functions of the form$\langle pp222\rangle$, extending the earlier result for $p=2$. As a byproductof our analysis, we also obtain explicit results for spinning four-pointfunctions of higher Kaluza-Klein modes.

Kaluza-Klein Five-Point Functions from $\textrm{AdS}_5\times S_5$ Supergravity