  We present the results of a study utilising ultra-deep, rest-frame UV,
spectroscopy to quantify the relationship between stellar mass and stellar
metallicity for 681 star-forming galaxies at $2.5<z<5.0$ ($\langle z \rangle =
3.5 \pm 0.6$) drawn from the VANDELS survey. Via a comparison with
high-resolution stellar population models, we determine stellar metallicities
for a set of composite spectra formed from subsamples selected by mass and
redshift. Across the stellar mass range $8.5 < \mathrm{log}(\langle M_{\ast}
\rangle/\rm{M}_{\odot}) < 10.2$ we find a strong correlation between stellar
metallicity and stellar mass, with stellar metallicity monotonically increasing
from $Z_{\ast}/\mathrm{Z}_{\odot} < 0.09$ at $\langle M_{\ast} \rangle = 3.2
\times 10^{8} \rm{M}_{\odot}$ to $Z_{\ast}/Z_{\odot} = 0.27$ at $\langle
M_{\ast} \rangle = 1.7 \times 10^{10} \rm{M}_{\odot}$. In contrast, at a given
stellar mass, we find no evidence for significant metallicity evolution across
the redshift range of our sample. However, comparing our results to the $z=0$
stellar mass-metallicity relation, we find that the $\langle z \rangle = 3.5$
relation is consistent with being shifted to lower metallicities by $\simeq
0.6$ dex. Contrasting our derived stellar metallicities with estimates of
gas-phase metallicities at similar redshifts, we find evidence for enhanced
$\rm{O}/\rm{Fe}$ ratios of the order (O/Fe) $\gtrsim 1.8$ $\times$
(O/Fe)$_{\odot}$. Finally, by comparing our results to simulation predictions,
we find that the $\langle z \rangle = 3.5$ stellar mass-metallicity relation is
consistent with current predictions for how outflow strength scales with galaxy
mass. This conclusion is supported by an analysis of analytic models, and
suggests that the mass loading parameter
($\eta=\dot{M}_{\mathrm{outflow}}/M_{\ast}$) scales as $\eta \propto
M_{\ast}^{\beta}$ with $\beta \simeq -0.4$.

Astrophysics of Galaxies