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We present a formula for the five-loop anomalous dimension of N=4 SYMtwist-three operators in the sl(2) sector. We obtain its asymptotic part fromthe Bethe Ansatz and finite volume corrections from the generalized Luescherformalism, considering scattering processes of spin chain magnons with virtualparticles that travel along the cylinder. The complete result respects theexpected large spin scaling properties and passes non-trivial tests includingreciprocity constraints. We analyze the pole structure and find agreement witha conjectured resummation formula. In analogy with the twist-two anomalousdimension at four-loops, wrapping effects are of order log^2 M/M^2 for largevalues of the spin.

Twist-three at five loops, Bethe Ansatz and wrapping