Assuming the coordinates are <E, N>, the total distance from the start is ...
5<5, -2> +<-1, 8> = <5·5 -1, 5(-2) +8> = <24, -2>
These coordinates represent a vector south of east, so the bearing measured clockwise from north will be greater than 90°. The reference angle (with respect to a north-south line) will be ...
The equation's slope is -4/10, which simplifies to -2/5. The reciprical of this, 5/2, is the slope of a perpendicular line. The first possibility you commented is the only one to have this slope.
