  In this work, the quasinormal modes of a $5$-D black hole in Einstein
Gauss-Bonnet Bumblebee theory of gravity have been investigated with the help
of the Pad\'e averaged higher order WKB approximation method and the validity
of Hod's conjecture has been studied. It is found that the presence of Lorentz
symmetry breaking due to the Bumblebee field favours Hod's conjecture. But in
the case of the Gauss-Bonnet term, an increase in the coupling parameter
increases the chances of violation of Hod's conjecture. We further investigated
the optical properties of the black hole {\it viz.}, shadow and emission rate.
It is found that a black hole with a lower lifetime favours Hod's conjecture.
