To isolate \( x \) in the equation \( x - \frac{7}{8} = -5 \), you want to add \( \frac{7}{8} \) to both sides of the equation. Doing so will give you:
\[ x - \frac{7}{8} + \frac{7}{8} = -5 + \frac{7}{8} \]
This simplifies to:
\[ x = -5 + \frac{7}{8} \]
Now, to find \( -5 + \frac{7}{8} \), first convert \(-5\) into a fraction with a denominator of 8:
\[ -5 = -\frac{40}{8} \]
Now, combine the fractions:
\[ x = -\frac{40}{8} + \frac{7}{8} = \frac{-40 + 7}{8} = \frac{-33}{8} \]
Thus, the number that should be added to both sides of the equation to solve for \( x \) is \( \frac{7}{8} \).