To make the subtraction sentence true, we start with the equation:
\[ x - 29 = -25 \]
We need to isolate \( x \). To do this, we can add 29 to both sides:
\[ x - 29 + 29 = -25 + 29 \]
This simplifies to:
\[ x = 4 \]
Therefore, the integer that makes the subtraction sentence true is \( 4 \).