ABSTRACT Recent Atacama Large Millimeter Array large surveys unveiled the presence of significant dust continuum emission in star-forming galaxies at z > 4. Unfortunately, such large programs – i.e. ALPINE (z ∼ 5) and REBELS (z ∼ 7) – only provide us with a single far-infrared (FIR) continuum data point for their individual targets. Therefore, high-z galaxies FIR spectral energy densities (SEDs) remain mostly unconstrained, hinging on an assumption for their dust temperature (Td) in the SED fitting procedure. This introduces uncertainties in the inferred dust masses (Md), infrared luminosities (LIR), and obscured star formation rate (SFR) fraction at z > 4. In this work, we use a method that allows us to constrain Td with a single-band measurement by combining the 158 $μ$m continuum information with the overlying [C ii emission line. We analyse the 21 [C ii and FIR continuum-detected z ∼ 5 galaxies in ALPINE, finding a range of Td = 25–60 K and Md = 0.6–25.1 × 107 M⊙. Given the measured stellar masses of ALPINE galaxies, the inferred dust yields are around Md/M⋆ = (0.2–8) × 10−3, consistent with theoretical dust-production constraints. We find that eight out of the 21 ALPINE galaxies have LIR ≥ 1012 L⊙, comparable to ultraluminous IR galaxies (ULIRGs). Relying on ultraviolet-to-optical SED fitting, the SFR was underestimated by up to two orders of magnitude in four of these eight ULIRGs-like galaxies. We conclude that these four peculiar sources should be characterized by a two-phase interstellar medium structure with ‘spatially segregated’ FIR and ultraviolet emitting regions.