  We study the threshold corrections to the structure functions in
deep-inelastic scattering (DIS) at the fifth logarithmic (N$^4$LL) order of the
soft-gluon exponentiation in massless perturbative QCD. Using recent results
for the splitting functions and the quark form factor, we derive the
fourth-order contribution to the coefficient $f^{\rm q}$ of the form factor and
from it the N$^4$LL part of the exponentiation coefficient $B^{\rm DIS}$ in the
limit of a large number of colours. An approximation scheme is shown that leads
to sufficiently accurate N$^4$LL results for full QCD. The N$^4$LL corrections
are small and lead to a further stabilization of the perturbative expansion for
the soft-gluon exponent.
