To determine the value of \( b \) from the equation \( b^3 = -125 \), we can take the cube root of both sides:
\[ b = \sqrt[3]{-125} \]
Calculating the cube root:
\[ b = -5 \]
Since \( (-5)^3 = -125 \), the solution is correct.
Thus, the value of \( b \) is:
\[ \boxed{-5} \]