5. Let $f(x)=x^{3}+\log _{2}\left(x+\sqrt{x^{2}+1}\right)$. Then for any real numbers $a, b, a+b \geqslant 0$ is a ( ) for $f(a)+f(b) \geqslant 0$.
(A) sufficient and necessary condition
(B) sufficient but not necessary condition
(C) necessary but not sufficient condition
(D) neither sufficient nor necessary condition