The propagation of a higher-order soliton in an ideal single-mode optical fibre under higher-order dispersion and higher-order nonlinearity is much affected by quintic nonlinearity, fourth-order dispersion and intrapulse Raman scattering. We use a compact split-step Padé scheme to numerically study the stabilisation ofhigher-order solitons by these effects in optical fibres. Our results show that the relative amplitudes of these two dispersive sideband waves, which originate from the fourth-order dispersion decrease or even eliminated by the increasing values of quintic nonlinear coefficient, in the presence of the intrapulse Raman scattering, and the higher-order soliton returns almost to its original shape.