Find $\mathbf{u}+\mathbf{v}$ \[ u=\langle 4,-5\rangle \text { and } \mathbf{v}=\langle-2,-3\rangle \] \[ \mathbf{u}+\mathbf{v}=\langle \] (Simplify your answers.)

Step 1 ：Given vectors are \(\mathbf{u} = \langle 4,-5 \rangle\) and \(\mathbf{v} = \langle -2,-3 \rangle\).

Step 2 ：The sum of two vectors is obtained by adding their corresponding components.

Step 3 ：Adding the corresponding components of vectors \(\mathbf{u}\) and \(\mathbf{v}\), we get \(\mathbf{u} + \mathbf{v} = \langle 4 + (-2), -5 + (-3) \rangle\).

Step 4 ：Simplifying the above expression, we get \(\mathbf{u} + \mathbf{v} = \langle 2, -8 \rangle\).

Step 5 ：\(\boxed{\mathbf{u} + \mathbf{v} = \langle 2, -8 \rangle}\)