  In this paper,linear constraint relations among loop-order five-point
color-ordered amplitudes in $SO(N)$ and $Sp(2N)$ gauge theories are derived
with the group-theoretic method. These constrains are derived up to four-loop
order. It is found that in both theories, there are $n=6,22,34,44,50$ linear
constraint relations at $L=0,1,2,3,4$ loop orders. Then the numbers of
independent color-ordered five-point amplitudes are respectively
$n_{ind.}=6,12,22,34,50$ at each loop order.
