To determine when the rational expression \(\frac{5x + 15}{-2x^2 - 16x - 32}\) is undefined, we need to find the values of \(x\) that make the denominator equal to zero.
First, we set the denominator to zero:
\[ -2x^2 - 16x - 32 = 0 \]
To simplify this, we can factor out \(-2\):
\[ -2(x^2 + 8x + 16) = 0 \]
Now, we solve the quadratic equation:
\[ x^2 + 8x + 16 = 0 \]
This can be factored as:
\[ (x + 4)(x + 4) = 0 \]
or
\[ (x + 4)^2 = 0 \]
Setting the factor equal to zero gives us:
\[ x + 4 = 0 \quad \Rightarrow \quad x = -4 \]
Thus, the value that would cause the rational expression to be undefined is:
\[ \boxed{-4} \]