Top quark mediated Higgs boson decay into hadrons to order alphas5.

We present in analytic form the O(alphas5) correction to the H-->gg partial width of the standard-model Higgs boson with an intermediate mass MH<2Mt. Its knowledge is useful because the O(alphas4) correction is sizable (around 20%). For MH=120 GeV, the resulting QCD correction factor reads 1+(215/12)alphas(5)(MH)/pi+152.5[alphas(5)(MH)/pi]2+381.5[alphas(5)(MH)/pi]3 approximately 1+0.65+0.20+0.02. The new four-loop correction increases the total Higgs-boson hadronic width by a small amount of order 1 per thousand and stabilizes significantly the residual scale dependence.