1. **State the problem:** We need to graph the function $f(x) = x^2 + 5$ as a translation of the parent function $g(x) = x^2$. 2. **Formula and rules:** The parent function is $g(x) = x^2$, a parabola with vertex at $(0,0)$. Adding a constant $c$ to the function, $f(x) = g(x) + c = x^2 + 5$, translates the graph vertically by $c$ units. 3. **Translation explanation:** Since $c=5$, the graph of $f(x)$ is the graph of $g(x)$ shifted 5 units up. 4. **Vertex of $f(x)$:** The vertex of $g(x)$ is at $(0,0)$, so the vertex of $f(x)$ is at $(0, 0+5) = (0,5)$. 5. **Graph features:** The parabola opens upward, same as $g(x)$, but shifted up. 6. **Final function for graphing:** $$f(x) = x^2 + 5$$ This is a solid curve parabola with vertex at $(0,5)$ opening upward. **Answer:** The graph of $f(x) = x^2 + 5$ is the parabola $y = x^2$ shifted 5 units up.