To solve for \( x \) in the equation
\[ \frac{x}{4} - 5 = -2, \]
first, add 5 to both sides of the equation:
\[ \frac{x}{4} - 5 + 5 = -2 + 5, \]
which simplifies to
\[ \frac{x}{4} = 3. \]
Next, to eliminate the fraction, multiply both sides by 4:
\[ 4 \cdot \frac{x}{4} = 4 \cdot 3, \]
which simplifies to
\[ x = 12. \]
Thus, the solution is
\[ \boxed{12}. \]