To find \((f \cdot g \cdot h)(x)\), we first need to multiply the three functions together.
Given:
- \( f(x) = -\sqrt[3]{x - 5} \)
- \( g(x) = 2\sqrt[3]{x - 5} \)
- \( h(x) = \sqrt[3]{x - 5} \)
Now, we will compute \((f \cdot g \cdot h)(x)\):
\[ (f \cdot g \cdot h)(x) = f(x) \cdot g(x) \cdot h(x) \]
Substituting the expressions for \( f(x) \), \( g(x) \), and \( h(x) \):
\[ = (-\sqrt[3]{x - 5}) \cdot (2\sqrt[3]{x - 5}) \cdot (\sqrt[3]{x - 5}) \]
Next, combine the cube root terms:
\[ = -2(\sqrt[3]{x - 5}) \cdot (\sqrt[3]{x - 5}) \cdot (\sqrt[3]{x - 5}) \]
This is equivalent to:
\[ = -2(\sqrt[3]{(x - 5)(x - 5)(x - 5)}) = -2\sqrt[3]{(x - 5)^3} \]
Since \(\sqrt[3]{(x - 5)^3} = x - 5\), we can simplify this further:
\[ = -2(x - 5) \]
Therefore, we have:
\[ (f \cdot g \cdot h)(x) = -2(x - 5) \]
So, the answer is:
\[ \boxed{-2(x - 5)} \]