  We give new explicit formulas for Grassmannian and Aomoto polylogarithms in
terms of iterated integrals, for arbitrary weight. We also explicitly reduce
the Grassmannian polylogarithm in weight 4 and in weight 5 each to depth 2.
Furthermore, using this reduction in weight 4 we obtain an explicit, albeit
complicated, form of the so-called 4-ratio, which gives an expression for the
Borel class in continuous cohomology of $\mathrm{GL}_4$ in terms of
$\mathrm{Li}_4$.
