  Fourier decay of fractal measures on surfaces plays an important role in
geometric measure theory and partial differential equations. In this paper, we
study the quadratic surfaces of high co-dimensions. Unlike the case of
co-dimension 1, quadratic surfaces of high co-dimensions possess some special
scaling structures and degenerate characteristics. We will adopt the strategy
from Du and Zhang, combined with the broad-narrow analysis with different
dimensions as divisions, to obtain a few lower bounds of Fourier decay of
fractal measures on quadratic surfaces of co-dimension two in $\mathbb{R}^5$.
