Let's simplify the expression step-by-step.
We start with the expression:
\[ \frac{-5(3 - \sqrt[3]{27} \cdot 2)}{3} \]
First, we can compute the cube root of \(27\):
\[ \sqrt[3]{27} = 3 \]
Now substitute this value back into the expression:
\[ \frac{-5(3 - 3 \cdot 2)}{3} \]
Next, simplify \(3 \cdot 2\):
\[ 3 \cdot 2 = 6 \]
Now substitute that into the expression:
\[ \frac{-5(3 - 6)}{3} \]
This simplifies to:
\[ \frac{-5(-3)}{3} \]
Now, simplify \(-5(-3)\):
\[ -5 \cdot -3 = 15 \]
We are left with:
\[ \frac{15}{3} \]
Finally, divide:
\[ \frac{15}{3} = 5 \]
Thus, the simplified expression is:
\[ \boxed{5} \]