1. **State the problem:** We need to find the sum of two vectors $\mathbf{s}$ and $\mathbf{t}$, where $\mathbf{s} = \langle 1, -4 \rangle$ and $\mathbf{t} = \langle -2, 5 \rangle$. 2. **Formula for vector addition:** The sum of two vectors $\mathbf{a} = \langle a_1, a_2 \rangle$ and $\mathbf{b} = \langle b_1, b_2 \rangle$ is given by: $$\mathbf{a} + \mathbf{b} = \langle a_1 + b_1, a_2 + b_2 \rangle$$ 3. **Apply the formula:** $$\mathbf{s} + \mathbf{t} = \langle 1 + (-2), -4 + 5 \rangle$$ 4. **Simplify the components:** $$\mathbf{s} + \mathbf{t} = \langle 1 - 2, -4 + 5 \rangle = \langle -1, 1 \rangle$$ 5. **Interpretation:** The vector sum $\mathbf{s} + \mathbf{t}$ points to the coordinates $(-1, 1)$ on the plane. **Final answer:** $$\mathbf{s} + \mathbf{t} = \langle -1, 1 \rangle$$