The first thing to do is to write the two formulas in the format of the equation of a line, y = mx + b
For x + 2y = 5 we will first get the y on the side by itself
2y = -x + 5
then divide both sides by 2
y = - 1/2 x + 5/2
For -2x - y = 5, get y by itself
-y = 2x +5
then multiply everything by -1 to get the y to a positive value
y = -2x - 5
Now we can compare the two equations. If two lines are parallel, then they must have the same slope. In these two line formulas, we see that one has slope of -1/2 and the other has a slope of -2 so they are not parallel.
For two lines to be perpendicular they would have the same value for the slope but have opposite signs (+/-) which is also not true in this case so the lines are neither perpendicular nor parallel.