To simplify the expression \( 20x^5 - 32x^5 \), we start by combining like terms:
\[ 20x^5 - 32x^5 = (20 - 32)x^5 = -12x^5 \]
Therefore, the simplified expression is:
\[ -12x^5 \]
From the responses you provided, the answer \( -12x^5 \) corresponds to the option:
\[ -12x^5 \]