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In previous work, the two-loop five-point amplitudes in $\mathcal{N}=4$ superYang-Mills theory and $\mathcal{N}=8$ supergravity were computed at symbollevel. In this paper, we compute the full functional form. The amplitudes areassembled and simplified using the analytic expressions of the two-looppentagon integrals in the physical scattering region. We provide the explicitfunctional expressions, and a numerical reference point in the scatteringregion. We then calculate the multi-Regge limit of both amplitudes. The resultis written in terms of an explicit transcendental function basis. For certainnon-planar colour structures of the $\mathcal{N}=4$ super Yang-Mills amplitude,we perform an independent calculation based on the BFKL effective theory. Wefind perfect agreement. We comment on the analytic properties of theamplitudes.

Multi-Regge Limit of the Two-Loop Five-Point Amplitudes in $\mathcal{N} = 4$ Super Yang-Mills and $\mathcal{N} = 8$ Supergravity