  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 ($M_\mathrm{stellar}$) 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-year
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 $3\sigma$ difference in the mass-step when comparing
blue ($c<0$) and red ($c>0$) SNe. We observe the lowest r.m.s. scatter
($\sim0.14$ 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 $M_\mathrm{stellar}$, approximating existing dust models,
we remove the mass-step from the data and find tentative $\sim 2\sigma$
residual steps in rest-frame galaxy $U-R$ colour. This indicates that dust
modelling based on $M_\mathrm{stellar}$ 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
$\leq1\sigma$ residual steps in $M_\mathrm{stellar}$ and local $U-R$,
suggesting that $U-R$ provides different information about the environment of
SNe Ia compared to $M_\mathrm{stellar}$, and motivating the inclusion of galaxy
$U-R$ colour in SN Ia distance bias correction.
