  Polytropic stars are useful tools for learning about stellar structure
without the complexity of comprehensive stellar models. These models rely on a
certain power-law correlation between the star's pressure and density. This
paper proposes a polytropic star model to investigate some new features in the
context of $5\mathcal{D}$ Einstein-Gauss-Bonnet (EGB) gravity using the
Finch-Skea {\em ansatz} [{\em M. R. Finch and J. E. Skea, Classical and Quantum
Gravity 6, 467 (1989)}]. Analytical results are better described by graphical
representations of the physical parameters for various values of the
Gauss-Bonnet coupling constant $\alpha$. The solution for a specific compact
object, EXO 1785-248, with radius $\mathfrak{R} = 8.849_{-0.04}^{+0.04}$ km and
mass $\mathcal{M} = 1.3 \pm 0.02~\mathcal{M}_{\odot}$, is shown here. We
analyze the essential physical attributes of the star, which reveal the
influence of the coupling parameter $\alpha$ on the values of the parameters.
Ultimately, we conclude that our current model is realistic because it
satisfies all the physical criteria for an acceptable model.
