To multiply \( 4 \) by \( -\frac{5}{8} \), we can express \( 4 \) as a fraction:
\[ 4 = \frac{4}{1} \]
Now, we can multiply the two fractions:
\[ \frac{4}{1} \times -\frac{5}{8} = \frac{4 \times -5}{1 \times 8} = \frac{-20}{8} \]
Next, we simplify \( \frac{-20}{8} \):
\[ \frac{-20 \div 4}{8 \div 4} = \frac{-5}{2} \]
Now, we convert \( \frac{-5}{2} \) to a mixed number. To do this, we divide \( -5 \) by \( 2 \):
\[ -5 \div 2 = -2 \quad \text{(whole number part)} \] with a remainder of \( 1 \).
This means:
\[ -5 = -2 \times 2 + 1 \]
So, the mixed number is:
\[ -2 \frac{1}{2} \]
Thus, the answer in simplest form as a mixed number is:
\[ \boxed{-2 \frac{1}{2}} \]