  Hybrid star is the term given to a neutron star with a quark core. Due to a
lot of uncertainties in the calculations and compositions of such a
high-density system, it is of great interest and a preferred scenario for
particle physicists and astrophysicists. To explore some novel aspects within
the framework of the $5\mathcal{D}$ Einstein-Gauss-Bonnet(EGB) gravity, our
current study presents a hybrid star model that includes strange quark matter
in addition to regular baryonic matter. In hybrid stellar objects, a hadronic
outer component surrounds a quark inner component, which prompts the
consideration of the most basic MIT bag model equation of state to correlate
the density and pressure of strange quark matter within the stellar interior,
while radial pressure and matter density due to baryonic matter are connected
by a linear equation of state. The model is constructed within the
specifications of the Krori and Barua (KB) {\em ansatz} (Krori and Barua, J.
Phys. A: Math. Gen. $\bold{8},508, 1975$). Here we present the solution for a
particular compact object 4U 1538 - 52 with mass $\mathcal{M} = 0.87 \pm
0.07~\mathcal{M}_{\odot}$ and radius $\mathfrak{R} = 7.866_{-0.21}^{+0.21}$ km.
We examine the fundamental physical characteristics of the star, which
highlights how the values of matter variables are affected by the Gauss-Bonnet
coupling parameter $\alpha$. Finally, as it meets all the physical requirements
for a realistic model, we have come to realize that our present model is
realistic.
