Okay, here we have this:
Considering that If two lines are parallel, their slopes are equal, we will calculate the slope of each one:
y=-1/5x-5: As follows the model y=mx+b, we can see that the slope is -1/5; therefore the line that is parallel to it must have the same slope:
Considering that the slope "m" of a line with the form Ax+By+C, is equals to -A/B, let's find it:
A 5x-y=-1:
m=-5/-1=5; This mean that option A is incorrect.
B 5x+y=3
m=-5/1=-5; This mean that option B is also incorrect.
C 5y-y=-10
4y=-10
y=0x-5/2
m=0; This mean that option C is also incorrect.
D x+5y=-30
m=-1/5; Finally we obtain that the correct answer is the option D.