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Dust is a key component of galaxies, but its properties during the earliest eras of structure formation remain elusive. Here we present a simple semi-analytic model of the dust distribution in galaxies at $z \gtrsim 5$. We calibrate the free parameters of this model to estimates of the UV attenuation (using the IRX-$\beta$ relation between infrared emission and the UV spectral slope) and to ALMA measurements of dust emission. We find that the observed dust emission requires that most of the dust expected in these galaxies is retained (assuming a similar yield to lower-redshift sources), but if the dust is spherically distributed, the modest attenuation requires that it be significantly more extended than the stars. Interestingly, the retention fraction is larger for less massive galaxies in our model. However, the required radius is a significant fraction of the host's virial radius and is larger than the estimated extent of dust emission from stacked high-$z$ galaxies. These can be reconciled if the dust is distributed anisotropically, with typical covering fractions of $\sim 0.2$--0.7 in bright galaxies and $\lesssim 0.1$ in fainter ones., Comment: 32 pages, 15 figures, submitted to JCAP