#### Answer

Neither parallel nor perpendicular.

#### Work Step by Step

We know that two parallel lines have the same slope ($m_1=m_2$).
We also know that perpendicular lines have negative reciprocal slopes ($m_1=-\frac{1}{m_2}$).
A line in slope-intercept form has the equation:
$y=mx+b$ ($m=slope$, $b=y-intercept$)
We put the line equations into slope-intercept form:
$4x+y=0$
$y=-4x$
$y=-4x+0$
$5x-8=2y$
$2y=5x-8$
$y=5/2x-4$
The two slopes ($5/2$ and $-4$) are not the same and not negative reciprocals. Thus the lines are neither parallel nor perpendicular.