I'll do substitution for you.
Lets flip the second equation around a little to make it x=-4y-8
Now plug it into the first equation.
2(-4y-8)+y=5
-8y-16+y=5
-7y=21
y=-3
Plug it back in to get x and then you solved the system.
2x-3=5
2x=8
x=4
So the solution to the system is
(4,-3)
Now to do it via elimination..
Lets get rid of the x to just leave the y
Multiply the second equation by -2..
2x+y=5
-2x-8y=16
combine like terms...
-7y=21
y=-3
plug it in again...
2x-3=5
2x=8
x=4
(4,-3)