Let \( \mathbf{e}_{1}=(1,0,0,0,0) \) and \( \mathbf{e}_{3}=(0,0,1,0,0) \), and define \( V \subseteq \mathbb{R}^{5} \) via
\[
V=\operatorname{span}\left(\mathbf{e}_{1}, \mathbf{e}_{3}\right)
\]
What is \( \operatorname{dim}\left(V^{\perp}\right) \) ?
Answer: \( \square \)