The opposite of 5 is -5. The absolute value of a number is always positive (e.g: |-10| = 10 because the negative sign is inside the absolute value bars).
-|5| and -|-5| both equal -5 because there is a negative sign outside of the bars. Since |-5| has a negative sign inside the bars, it equals 5.
I tried hard to explain this, so I hope it makes sense! :)
