Let $C$ be the straight line curve between the points $(0,5)$ and $(1,0)$. Let the unit normal vector field $N$ on $C$ be oriented away from the origin. Let $F: \mathbb{R}^2\to\mathbb{R}^2$ be the vector field defined by $F(x,y)=(x,12)$. Find the flux of $F$ across the curve $C$ in the direction pointing away from the origin.
$\int_C F\cdot N =$