  We obtain all planar four-point correlators of half-BPS operators in
$\mathcal{N}=4$ SYM up to five loops. The ansatz for the integrand is fixed
partially by imposing light-cone OPE relations between different correlators.
We then fix the integrated correlators by comparing their asymptotic expansions
with simple data obtained from integrability. We extract OPE coefficients and
find a prediction for the triple wrapping correction of the hexagon form
factors, which contributes already at the five-loop order.
