To multiply \(4\) by \(-\frac{5}{8}\), we can first express \(4\) as a fraction:
\[ 4 = \frac{4}{1} \]
Now we multiply the fractions:
\[ \frac{4}{1} \times -\frac{5}{8} = \frac{4 \times -5}{1 \times 8} = \frac{-20}{8} \]
Next, we simplify \(\frac{-20}{8}\):
\[ \frac{-20}{8} = \frac{-20 \div 4}{8 \div 4} = \frac{-5}{2} \]
Now we will convert \(\frac{-5}{2}\) into a mixed number. To do this, we divide \(5\) by \(2\):
\[ 5 \div 2 = 2 \quad \text{remainder } 1 \]
Thus, we have:
\[ \frac{-5}{2} = -2 \frac{1}{2} \]
Therefore, the answer as a mixed number in simplest form is:
\[ \boxed{-2 \frac{1}{2}} \]