  We develop new techniques to compute five-point correlation functions from
IIB supergravity on $AdS_5\times S^5$. Our methods rely entirely on symmetry
and general consistency conditions, and eschew detailed knowledge of the
supergravity effective action. We demonstrate our methods by computing the
five-point function of the $\mathbf{20'}$ operator, which is the superconformal
primary of the stress tensor multiplet. We also develop systematic methods to
compute the five-point conformal blocks in series expansions. Using the
explicit expressions of the conformal blocks, we perform a Euclidean OPE
analysis of the $\mathbf{20'}$ five-point function. We find expected agreement
with non-renormalized quantities and also extract new CFT data at strong
coupling.
