>>14427915observe that -5 is exactly a half rotation (180 degrees) from 5 on the number line, multiplying by minus 1 is always a half turn.
Draw it out on a piece of paper.
Now make a rotation from minus 5, where are you gonna end up at?
This is the intuitive way to see it but if you want a boring formal way, -1*x is the additive inverse of x for all x, take x=-a and voila.
Alternatively, -(-x) + (-x)=-(-x) - x=0, as you can see, necessarily -(-x) must be equal to x for the result to be true.
