(5) A line $l$ passing through the origin $O$ intersects the ellipse $C: \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1(a>b>0)$ at points $M$ and $N$, and $P$ is any point on the ellipse $C$ different from $M$ and $N$. If the product of the slopes of the lines $PM$ and $PN$ is $-\frac{1}{3}$, then the eccentricity of the ellipse $C$ is $\qquad$.
(5) $\frac{\sqrt{6}}{3}$