  Supersymmetric integrands for the two-loop five-point amplitudes in
ten-dimensional super Yang--Mills and type II supergravity are proposed. The
kinematic numerators are manifestly local and satisfy the duality between color
and kinematics described by Bern, Carrasco and Johansson. Our results are
expected to reproduce the integrated two-loop amplitudes in dimensions $D<7$.
The UV divergence in the critical dimension $D=7$ matches the low-energy limit
of the corresponding superstring amplitudes and is written in terms of SYM tree
amplitudes.
