The rational expression \( \frac{5x + 15}{-2x^2 - 16x - 32} \) is undefined when the denominator is equal to zero.
To find the value(s) of \( x \) that cause the expression to be undefined, we need to set the denominator equal to zero and solve for \( x \):
\[ -2x^2 - 16x - 32 = 0 \]
Dividing each term by -2 gives:
\[ x^2 + 8x + 16 = 0 \]
Now, we can factor the quadratic expression:
\[ (x + 4)(x + 4) = 0 \quad \text{or} \quad (x + 4)^2 = 0 \]
Setting the factor equal to zero gives us:
\[ x + 4 = 0 \quad \Rightarrow \quad x = -4 \]
Thus, the rational expression is undefined at \( x = -4 \).
So the answer is:
\[ x = -4 \]