To solve the equation
\[ -\frac{b}{5} - 27 = -21, \]
first, we can isolate the term involving \(b\). Start by adding 27 to both sides:
\[ -\frac{b}{5} - 27 + 27 = -21 + 27. \]
This simplifies to:
\[ -\frac{b}{5} = 6. \]
Next, to eliminate the negative sign, multiply both sides by -1:
\[ \frac{b}{5} = -6. \]
Now, to solve for \(b\), multiply both sides by 5:
\[ b = -6 \cdot 5. \]
Calculating the right side gives:
\[ b = -30. \]
Thus, the solution is
\[ \boxed{-30}. \]