To solve the equation \( x - 78 = -5 \), we need to isolate \( x \). To do this, we can add 78 to both sides of the equation:
\[ x - 78 + 78 = -5 + 78 \]
This simplifies to:
\[ x = 73 \]
So, to determine what number should be added to both sides of the equation to find the value of \( x \), the answer is 78.