#### Answer

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:
$2x+5y=-7$
$5y=-7-2x$
$y=(-7-2x)/5$
$y=-\frac{7}{5}-\frac{2}{5}x$
$y=-\frac{2}{5}x-\frac{7}{5}$
$5x-2y=1$
$-2y=1-5x$
$y=(1-5x)/-2$
$y=-\frac{1}{2}+\frac{5}{2}x$
$y=\frac{5}{2}x-\frac{1}{2}$
The two slopes (-$\displaystyle \frac{2}{5}$ and $\displaystyle \frac{5}{2}$) are negative reciprocals of each other. Thus the lines are perpendicular.