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Of the almost 40 star-forming galaxies at z≳ 5 (not counting quasi-stellar objects) observed in [{{C}} {{II}}] to date, nearly half are either very faint in [{{C}} {{II}}] or not detected at all, and fall well below expectations based on locally derived relations between star formation rate and [{{C}} {{II}}] luminosity. This has raised questions as to how reliable [{{C}} {{II}}] is as a tracer of star formation activity at these epochs and how factors such as metallicity might affect the [{{C}} {{II}}] emission. Combining cosmological zoom simulations of galaxies with SÍGAME (SImulator of GAlaxy Millimeter/submillimeter Emission), we modeled the multiphased interstellar medium (ISM) and its emission in [{{C}} {{II}}], as well as in [O I] and [O III], from 30 main-sequence galaxies at z≃ 6 with star formation rates ˜3-23 {M}⊙ {yr}}-1, stellar masses ˜ (0.7{--}8)× {10}9 {M}⊙ , and metallicities ˜ (0.1{--}0.4)× {Z}⊙ . The simulations are able to reproduce the aforementioned [{{C}} {{II}}] faintness of some normal star-forming galaxy sources at z≥slant 5. In terms of [O I] and [O III], very few observations are available at z≳ 5, but our simulations match two of the three existing z≳ 5 detections of [O III] and are furthermore roughly consistent with the [O I] and [O III] luminosity relations with star formation rate observed for local starburst galaxies. We find that the [{{C}} {{II}}] emission is dominated by the diffuse ionized gas phase and molecular clouds, which on average contribute ˜66% and ˜27%, respectively. The molecular gas, which constitutes only ˜ 10 % of the total gas mass, is thus a more efficient emitter of [{{C}} {{II}}] than the ionized gas, which makes up ˜85% of the total gas mass. A principal component analysis shows that the [{{C}} {{II}}] luminosity correlates with the star formation activity of a galaxy as well as its average metallicity. The low metallicities of our simulations together with their low molecular gas mass fractions can account for their [{{C}} {{II}}] faintness, and we suggest that these factors may also be responsible for the [{{C}} {{II}}]-faint normal galaxies observed at these early epochs.