Answer
The angle of the displacement vector is $~~-45^{\circ}~~$ relative to the positive x direction.
Work Step by Step
The initial position is $~~r_i = (-5.0~m)\hat{i}+(8.0~m)\hat{j}$
The final position is $~~r_f = (3.00~m)\hat{i}$
We can find the displacement:
$\Delta r = r_f - r_i$
$\Delta r = (8.0~m)\hat{i}-(8.0~m)\hat{j}$
By symmetry, we can see that the angle of the displacement vector is $~~-45^{\circ}~~$ relative to the positive x direction.
