(5) Given that $A, B, C$ are three points on the ellipse $\frac{x^{2}}{25}+\frac{y^{2}}{16}=1$, and point $F(3,0)$. If $\overrightarrow{F A}+\overrightarrow{F B}+\overrightarrow{F C}=\mathbf{0}$, then $|\overrightarrow{F A}|+|\overrightarrow{F B}|+|\overrightarrow{F C}|=$ $\qquad$ .
(5) $\frac{48}{5}$