jmc

First, we would like to find where $y=5x+3$ and $y=-2x-25$ intersect. We can represent this geometric intersection by setting the $y$'s equal to each other, giving $5x+3=-2x-25$. Solving this yields $x=-4$, so $y=5\cdot (-4)+3$, or $y=-17$. Now, we can plug $x$ and $y$ into the last equation to solve for $k$: $-17=-12+k$, so $k=\boxed{-5}$.