ABSTRACT Recent observations indicate that galactic outflows are ubiquitous in high-redshift (high-z) galaxies, including normal star-forming galaxies, quasar hosts, and dusty star-forming galaxies (DSFGs). However, the impact of outflows on the evolution of their hosts is still an open question. Here, we analyse the star-formation histories and galactic outflow properties of galaxies in massive haloes ($10^{12}\, {\rm M}_{\odot }\ \lt\ M_{\rm vir}\ \lt\ 5\times 10^{12}\, {\rm M}_{\odot }$) at z ≳ 5.5 in three zoom-in cosmological simulations from the MassiveFIRE suite, as part of the Feedback In Realistic Environments (FIRE) project. The simulations were run with the FIRE-2 model, which does not include feedback from active galactic nuclei. The simulated galaxies resemble z > 4 DSFGs, with star-formation rates of $\sim\!{1000}\ {\rm M}_{\odot }\, \rm yr^{-1}$ and molecular gas masses of Mmol ∼ 1010 M⊙. However, the simulated galaxies are characterized by higher circular velocities than those observed in high-z DSFGs. The mass loading factors from stellar feedback are of the order of ∼0.1, implying that stellar feedback is inefficient in driving galactic outflows and gas is consumed by star formation on much shorter time-scales than it is expelled from the interstellar medium. We also find that stellar feedback is highly inefficient in self-regulating star formation in this regime, with an average integrated star formation efficiency (SFE) per dynamical time of 30 per cent. Finally, compared with FIRE-2 galaxies hosted in similarly massive haloes at lower redshift, we find lower mass loading factors and higher SFEs in the high-z sample. We argue that both effects originate from the higher total and gas surface densities that characterize high-z massive systems.