Consider a function \( g(x) \) defined for \( x \in \mathbb{R} \) that satisfies the following properties:
1. \( g(x) \) is monotonic, meaning \( g(x) \leq g(y) \) for all \( x \leq y \).
2. \( g(x) \) is symmetric around \( x = 0 \), which means \( g(x) = g(-x) \).

Given that \( g(2) = 5 \), find the value of \( g(-4) + g(4) \). Let's think step by step and output the final answer within \boxed{}.
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