Recent analyses have found intriguing correlations between the colour (c) of type Ia supernovae (SNe Ia) and the size of their ‘mass-step’, the relationship between SN Ia host galaxy stellar mass (Mstellar) and SN Ia Hubble residual, and suggest that the cause of this relationship is dust. Using 675 photometrically classified SNe Ia from the Dark Energy Survey 5-yr sample, we study the differences in Hubble residual for a variety of global host galaxy and local environmental properties for SN Ia subsamples split by their colour. We find a 3σ difference in the mass-step when comparing blue (c < 0) and red (c > 0) SNe. We observe the lowest r.m.s. scatter (∼0.14 mag) in the Hubble residual for blue SNe in low mass/blue environments, suggesting that this is the most homogeneous sample for cosmological analyses. By fitting for c-dependent relationships between Hubble residuals and Mstellar, approximating existing dust models, we remove the mass-step from the data and find tentative ∼2σ residual steps in rest-frame galaxy U − R colour. This indicates that dust modelling based on Mstellar may not fully explain the remaining dispersion in SN Ia luminosity. Instead, accounting for a c-dependent relationship between Hubble residuals and global U − R, results in ≤1σ residual steps in Mstellar and local U − R, suggesting that U − R provides different information about the environment of SNe Ia compared to Mstellar, and motivating the inclusion of galaxy U − R colour in SN Ia distance bias correction.