Notice that the given function is a form of an absolute value function.
The standard form of an absolute value function is y = a|x - h| + k, where (h, k) is the vertex of the absolute value function.
In this case, x + 5 can be rewritten as x - (-5). Therefore, h = -5.
The constant term outside the absolute value function is +7, which represents k.
The vertex (h, k) of the function g(x) is (-5, 7).
From the provided options, the correct answer is D.
