The creep behaviour of directionally solidified SAC305 (96.5Sn-3Ag-0.5Cu wt%) alloy has been investigated with integrated particle matrix composite (PMC) crystal plasticity modelling and quantitative experimental characterisation and test. In this manuscript, the mechanistic basis of creep rate dependence is shown to be influenced by plastic strain gradients, and the associated hardening due to geometrically necessary dislocation (GND) density. These gradients are created due to heterogenous deformation at the Sn phase and intermetallic compound (IMCs) boundaries. The size and distribution of IMCs is important, as finer and well dispersed IMCs leading to higher creep resistance and lower creep rates, and this agrees with experimental observations. This understanding has enabled the creation of a new microstructurally homogenized model which captures this mechanistic link between the GND hardening, the intermetallic size, and the corresponding creep rate. The homogenised model relates creep rates to the microstructure found within the solder alloy as they evolve in service, when ageing and coarsening kinetics are known.