5 Let $f(x)=x^{3}+\log _{2}\left(x+\sqrt{x^{2}+1}\right)$, then for any real numbers $\dot{a}, b$, $a+b \geqslant 0$ 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