$$\vec{A} = -5\hat{i} + 4\hat{j}$$
$$\vec{B} = 3\hat{i} + 5\hat{j}$$
Imagine you wanted to add $$\vec{A}$$ and $$\vec{B}$$. The resultant vector would simply be
$$\vec{C} = \vec{A} + \vec{B}$$ $$= (-5\hat{i} + 4\hat{j}) + (3\hat{i} + 5\hat{j})$$
$$= -2\hat{i} + 9\hat{j}$$