  A core challenge in understanding high entropy oxides (HEOs) is how these
systems, with five or more cations at a crystallographic site, can withstand
local distortions while preserving a uniform structure on a larger scale. We
address this for spinel HEO by comparatively examining extended X-ray
absorption fine structure (EXAFS) on
(Mn$_{0.2}$Co$_{0.2}$Ni$_{0.2}$Cu$_{0.2}$Zn$_{0.2}$)Cr$_2$O$_4$
($A^5$Cr$_2$O$_4$) and its parent counterparts $A$Cr$_2$O$_4$ ($A$= Mn, Co, Ni,
Cu, Zn). Unlike the HEO with rock-salt structure, the element-specific
distortions in disordered sublattice go beyond the first neighbor here.
Moreover, the tetragonal distortion around the Cu$^{2+}$ ion, known as a
textbook example of the Jahn-Teller effect, is highly reduced in
$A^5$Cr$_2$O$_4$ compared to CuCr$_2$O$_4$. Despite variations in the A-O bond
lengths, the inter-cationic distances remained remarkably similar. This affirms
a high level of flexibility in the positioning of oxygen, enabling them to
adapt to the overall cubic symmetry. Despite containing multiple magnetic ions,
the Curie-Weiss temperature and effective magnetic moments of $A^5$Cr$_2$O$_4$
are similar to those of NiCr$_2$O$_4$. This can be attributed to both
materials' comparable local bond lengths around Cr, as evidenced by EXAFS
analysis. This study conclusively presents a method for elucidating how local
structural distortions influence the macroscopic properties of compositionally
complex quantum materials.
