To find the value that would make the rational expression \(\frac{5x + 15}{-2x^2 - 16x - 32}\) undefined, we need to determine when the denominator equals zero.
Let's set the denominator equal to zero:
\[ -2x^2 - 16x - 32 = 0 \]
To make this simpler, we can divide the entire equation by -2:
\[ x^2 + 8x + 16 = 0 \]
Now, we can factor the quadratic:
\[ (x + 4)(x + 4) = 0 \]
This gives us:
\[ (x + 4)^2 = 0 \]
So, \(x + 4 = 0\) gives us:
\[ x = -4 \]
Thus, the rational expression is undefined when:
\[ \boxed{-4} \]