\section*{5. C}
Solution: By the property of ellipses, $\left| M F _ { 1 } \right| + \left| M F _ { 2 } \right| = 2 a = 6$. By the AM-GM inequality:
$$\left| M F _ { 1 } \right| \cdot \left| M F _ { 2 } \right| \leq \frac { 1 } { 4 } \left( \left| M F _ { 1 } \right| + \left| M F _ { 2 } \right| \right) ^ { 2 } = 9 .$$
Equality holds when $\left| M F _ { 1 } \right| = \left| M F _ { 2 } \right| = 3$, and $M$ is the upper or lower vertex of the ellipse. So the answer is $C$.