Control of the size and agglomeration of micellar systems is important for pharmaceutical applications such as drug delivery. Although shape-related transitions in surfactant solutions are studied experimentally, their molecular mechanisms are still not well understood. In this study, we use coarse-grained molecular dynamics simulations to describe micellar assemblies of pentaethylene glycol monododecyl ether (C12E5) in aqueous solution at different concentrations. The obtained size and aggregation numbers of the aggregates formed are in very good agreement with the available experimental data. Importantly, increase of the concentration leads to a second critical micelle concentration where a transition to rod-like aggregates is observed. This transition is quantified in terms of shape anisotropy, together with a detailed structural analysis of the micelles as a function of aggregation number.