The problem asks to identify the graph of the function $f(x) = x^2 + 5$.

1. Problem Description

The problem asks to identify the graph of the function $f(x) = x^2 + 5$.

2. Solution Steps

The given function is $f(x) = x^2 + 5$. This is a quadratic function in the form $f(x) = ax^2 + bx + c$, where $a=1$, $b=0$, and $c=5$. Since $a > 0$, the parabola opens upwards. The vertex of the parabola is at the point $(-\frac{b}{2a}, f(-\frac{b}{2a}))$. In this case, the x-coordinate of the vertex is $-\frac{0}{2(1)} = 0$. The y-coordinate of the vertex is $f(0) = 0^2 + 5 = 5$. Thus, the vertex is at $(0, 5)$. The graph of $f(x) = x^2$ is a parabola with its vertex at the origin (0, 0). The graph of $f(x) = x^2 + 5$ is the graph of $f(x) = x^2$ shifted upwards by 5 units.

3. Final Answer

The graph is a parabola opening upwards with its vertex at (0, 5).