We present the results of a study investigating the dust attenuation law at z ≃ 5, based on synthetic spectral energy distributions (SEDs) calculated for a sample of N = 498 galaxies drawn from the First Billion Years (FiBY) simulation project. The simulated galaxies at z ≃ 5, which have M1500 ≤ -18.0 and 7.5 ≤ log(M/M}_{⊙}) ≤ 10.2, display a mass-dependent α-enhancement, with a median value of [α /{Fe}]_{z=5} ˜eq 4 × [α /{Fe}]_{Z_{⊙}}. The median Fe/H ratio of the simulated galaxies is 0.14 ± 0.05 which produces steep intrinsic ultraviolet (UV) continuum slopes; 〈βi〉 = -2.4 ± 0.05. Using a set of simple dust attenuation models, in which the wavelength-dependent attenuation is assumed to be of the form A(λ) ∝ λn, we explore the parameter values which best reproduce the observed z = 5 luminosity function (LF) and colour-magnitude relation (CMR). We find that a simple model in which the absolute UV attenuation is a linearly increasing function of log stellar mass (A1500 = 0.5 × log(M/M⊙) - 3.3), and the dust attenuation slope (n) is within the range -0.7 ≤ n ≤ -0.3, can successfully reproduce the LF and CMR over a wide range of stellar population synthesis model assumptions, including the effects of massive binaries. This range of attenuation curves is consistent with a power-law fit to the Calzetti attenuation law in the UV (n = -0.55). In contrast, curves as steep as the Small Magellanic Cloud extinction curve (n = -1.24) are formally ruled out. Finally, we show that our models are consistent with recent 1.3 mm Atacama Large Millimeter Array observations of the Hubble Ultra Deep Field, and predict the form of the z ≃ 5 infrared excess (IRX)-β relation.