Two lines
g: y = mx+b
h: y = nx+a
Are perpendicular if m = -1/n or if m*n =(-1).
Bothe the statements are equivalent, it might just be easier for you to work with the latter.
Now, in our definition both lines were given with respect to y. Here that is not the case, as the second line is not given with respect to y. So we do some reordering:
10x+2y=0
2y = -10x
y = -5x
Now, as you can see, for the first line m=5, for the second one n = -5, but m*n = 5*(-5)=-25 is not -1 so these lines are not perpendicular.
Is there maybe a typo somewhere in your message?