  We present a new method for computing the Konishi anomalous dimension in N=4
SYM at weak coupling. It does not rely on the conventional Feynman diagram
technique and is not restricted to the planar limit. It is based on the OPE
analysis of the four-point correlation function of stress-tensor multiplets,
which has been recently constructed up to six loops. The Konishi operator gives
the leading contribution to the singlet SU(4) channel of this OPE. Its
anomalous dimension is the coefficient of the leading single logarithmic
singularity of the logarithm of the correlation function in the double
short-distance limit, in which the operator positions coincide pairwise. We
regularize the logarithm of the correlation function in this singular limit by
a version of dimensional regularization. At any loop level, the resulting
singularity is a simple pole whose residue is determined by a finite two-point
integral with one loop less. This drastically simplifies the five-loop
calculation of the Konishi anomalous dimension by reducing it to a set of known
four-loop two-point integrals and two unknown integrals which we evaluate
analytically. We obtain an analytic result at five loops in the planar limit
and observe perfect agreement with the prediction based on integrability in
AdS/CFT.
