Soft corrections to inclusive DIS at four loops and beyond

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 fourthorder contribution to the coefficient f${}^q$ of the form factor and from it the N${}^4$LL part of the exponentiation coefficient B${}^{DIS}$ 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.