The Swift era has posed a challenge to the standard blast-wave model of gamma-ray burst (GRB) afterglows. The key observational features expected within the model are rarely observed, such as the achromatic steepening (‘jet break’) of light curves. The observed afterglow light curves showcase additional complex features requiring modifications within the standard model. Here we present optical/near-infrared observations, millimetre upper limits and comprehensive broad-band modelling of the afterglow of the bright GRB 0505025A, detected by Swift. This afterglow cannot be explained by the simplistic form of the standard blast-wave model. We attempt modelling multiwavelength light curves using (i) a forward–reverse shock model, (ii) a two-component outflow model and (iii) a blast-wave model with a wind termination shock. The forward–reverse shock model cannot explain the evolution of the afterglow. The two-component model is able to explain the average behaviour of the afterglow very well but cannot reproduce the fluctuations in the early X-ray light curve. The wind termination shock model reproduces the early light curves well but deviates from the global behaviour of the late-time afterglow.