  In recent years, there has been a growing interest in stellar modelling in
the framework of Einstein-Gauss-Bonnet gravity. In this paper, for a
relativistic star in static equilibrium, we invoke the $5$ dimensional
Einstein-Gauss-Bonnet gravity and solve the system by assuming a matter
distribution that admits a linear equation of state (EOS). We fix the model
parameters by matching the interior solution to the exterior Boulware-Deser
metric which facilitates physical analysis of the resultant configuration. We
analyze the star's gross physical properties, which brings to attention the
role of the Gauss-Bonnet coupling parameter $\alpha$ in fine-tuning the values
of the matter variables.
