To solve the equation \( x - 78 = -5 \), you want to isolate \( x \). One way to do this is by adding 78 to both sides of the equation.
So, you should add \( 78 \) to both sides:
\[ x - 78 + 78 = -5 + 78 \]
This simplifies to:
\[ x = 73 \]
Therefore, the number that should be added to both sides of the equation is \( 78 \).