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We present the results of 3D, flux-driven, global, two-fluid electrostatic turbulence simulations in a 5-field period stellarator with an island divertor. The numerical simulations are carried out with the GBS code, which solves the two-fluid drift-reduced Braginskii equations and has been extended recently to simulate plasma turbulence in non-axisymmetric magnetic equilibria. The vacuum magnetic field used in the simulations is carefully constructed using Dommaschk potentials in order to describe a configuration with a central region of nested flux surfaces, surrounded by a chain of magnetic islands. In a similar way to the diverted configurations of W7-AS and W7-X, particles and heat, transported radially outwards from the core region, reach the island region, which effectively acts as a scrape-off-layer with the open field lines striking the walls at specific toroidal locations of the device wall. We find that the radial particle and heat transport is mainly driven by a field-aligned mode with low poloidal wavenumber, whose origin is investigated theoretically. The equilibrium radial electric field in the core is found to be in the ion-root regime, Er