Please note that this is explained in the step explanation (see below)

The rule is that when you move a term from one side to the other , the term changes the sign.

The reason behind this is the following:

You don't actually 'move' terms; that is just a shorthand. What really happens is that you apply the same operation on both sides of equation. So, for example, '-5' is added to both sides. On the left side, this has the effect of removing the existing +5  (-5+5=0), and on the right side it simply stays as '-5'

Regards,

NJ