To solve the equation \( x - \frac{7}{8} = -5 \), we want to isolate \( x \).
First, let's add \( \frac{7}{8} \) to both sides of the equation:
\[ x - \frac{7}{8} + \frac{7}{8} = -5 + \frac{7}{8} \]
This simplifies to:
\[ x = -5 + \frac{7}{8} \]
To combine \( -5 \) and \( \frac{7}{8} \), we can convert \( -5 \) into a fraction with a denominator of 8:
\[ -5 = -\frac{40}{8} \]
Now we can add the two fractions:
\[ x = -\frac{40}{8} + \frac{7}{8} = \frac{-40 + 7}{8} = \frac{-33}{8} \]
Thus, the value for \( x \) is \( \frac{-33}{8} \).
To answer the original question, the number that should be added to both sides of the equation is \( \frac{7}{8} \).