A parabola with equation $ y \equal{} ax^2 \plus{} bx \plus{} c$ is reﬂected about the $ x$-axis. The parabola and its reﬂection are translated horizontally ﬁve units in opposite directions to become the graphs of $ y \equal{} f(x)$ and $ y \equal{} g(x)$, respectively. Which of the following describes the graph of $ y \equal{} (f \plus{} g)(x)$? 

$ \textbf{(A)}\ \text{a parabola tangent to the }x\text{ \minus{} axis}$
$ \textbf{(B)}\ \text{a parabola not tangent to the }x\text{ \minus{} axis} \qquad \textbf{(C)}\ \text{a horizontal line}$
$ \textbf{(D)}\ \text{a non \minus{} horizontal line} \qquad \textbf{(E)}\ \text{the graph of a cubic function}$
1. Given the equation of the parabola \( y = ax^2 + bx + c \), we first reflect it about the \( x \)-axis. The reflection of \( y = ax^2 + bx + c \) about the \( x \)-axis is \( y = -ax^2 - bx - c \).

2. Let \( f(x) = ax^2 + bx + c \) and \( g(x) = -ax^2 - bx - c \).

3. Next, we translate \( f(x) \) horizontally by 5 units to the left. The translated function is:
   \[
   f(x+5) = a(x+5)^2 + b(x+5) + c
   \]
   Expanding this, we get:
   \[
   f(x+5) = a(x^2 + 10x + 25) + b(x + 5) + c = ax^2 + 10ax + 25a + bx + 5b + c
   \]
   Simplifying, we have:
   \[
   f(x+5) = ax^2 + (10a + b)x + (25a + 5b + c)
   \]

4. Similarly, we translate \( g(x) \) horizontally by 5 units to the right. The translated function is:
   \[
   g(x-5) = -a(x-5)^2 - b(x-5) - c
   \]
   Expanding this, we get:
   \[
   g(x-5) = -a(x^2 - 10x + 25) - b(x - 5) - c = -ax^2 + 10ax - 25a - bx + 5b - c
   \]
   Simplifying, we have:
   \[
   g(x-5) = -ax^2 + (10a - b)x + (-25a + 5b - c)
   \]

5. Now, we find \( (f + g)(x) \):
   \[
   (f + g)(x) = f(x+5) + g(x-5)
   \]
   Substituting the expanded forms of \( f(x+5) \) and \( g(x-5) \):
   \[
   (f + g)(x) = [ax^2 + (10a + b)x + (25a + 5b + c)] + [-ax^2 + (10a - b)x + (-25a + 5b - c)]
   \]
   Combining like terms, we get:
   \[
   (f + g)(x) = ax^2 - ax^2 + (10a + b)x + (10a - b)x + (25a + 5b + c) + (-25a + 5b - c)
   \]
   Simplifying further:
   \[
   (f + g)(x) = 0x^2 + (10a + b + 10a - b)x + (25a + 5b + c - 25a + 5b - c)
   \]
   \[
   (f + g)(x) = 20ax + 10b
   \]

6. The resulting function \( y = (f + g)(x) = 20ax + 10b \) is a linear function with slope \( 20a \) and y-intercept \( 10b \).

Conclusion:
The graph of \( y = (f + g)(x) \) is a non-horizontal line.

The final answer is \( \boxed{ \text{a non-horizontal line} } \)