To simplify the expression \(-5^4\), we need to evaluate \(5^4\) first and then apply the negative sign.
Calculating \(5^4\):
\[ 5^4 = 5 \times 5 \times 5 \times 5 = 625 \]
Now, applying the negative sign:
\[ -5^4 = -625 \]
Thus, the simplified expression is:
\[ \boxed{-625} \]