  Integrands for colour ordered scattering amplitudes in planar N=4 SYM are
dual to those of correlation functions of the energy-momentum multiplet of the
theory. The construction can relate amplitudes with different numbers of legs.
  By graph theory methods the integrand of the four-point function of
energy-momentum multiplets has been constructed up to six loops in previous
work. In this article we extend this analysis to seven loops and use it to
construct the full integrand of the five-point amplitude up to five loops, and
in the parity even sector to six loops.
  All results, both parity even and parity odd, are obtained in a concise local
form in dual momentum space and can be displayed efficiently through graphs. We
have verified agreement with other local formulae both in terms of
supertwistors and scalar momentum integrals as well as BCJ forms where those
exist in the literature, i.e. up to three loops.
  Finally we note that the four-point correlation function can be extracted
directly from the four-point amplitude and so this uncovers a direct link from
four- to five-point amplitudes.
