Top Quark Mediated Higgs Decay into Hadrons to Order alpha(s)**5

We present in analytic form the O(alpha_s^5) correction to the H->gg partial width of the standard-model Higgs boson with intermediate mass M_H<2M_t. Its knowledge is useful because the O(alpha_s^4) correction is sizeable (around 20%). For M_H=120 GeV, the resulting QCD correction factor reads 1 + (215/12) alpha_s^(5)(M_H)/pi + 152.5 (alpha_s^(5)(M_H)/pi)^2 + 381.5 (alpha_s^(5)(M_H)/pi)^3 \approx 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 promille and stabilizes significantly the residual scale dependence.