5. Vitya and Misha argued: the first of them claimed that if $a=|b|$, then the equality $a+b=0$ is always true; the second, however, said that this equality is always false. Who is right?
5. If $b \leqslant 0$, then $a+b=|b|+b=0$; if $b>0$, then $a+b=2 b \neq 0$. Therefore, neither of the boys is correct.