Evaluate \( \frac{1}{5} y z \) if \( y=\frac{4}{5} \) and \( z=-1 \frac{5}{8} \). Write in simplest form.

To evaluate \( \frac{1}{5} y z \) with \( y=\frac{4}{5} \) and \( z=-1 \frac{5}{8} \), we first convert \( z \) into an improper fraction. The mixed number \(-1 \frac{5}{8}\) can be expressed as \[ -1 - \frac{5}{8} = -\frac{8}{8} - \frac{5}{8} = -\frac{13}{8}. \] Next, we plug in the values of \( y \) and \( z \): \[ \frac{1}{5} \cdot \frac{4}{5} \cdot \left(-\frac{13}{8}\right). \] Now, let's multiply these fractions: 1. Multiply the numerators: \[ 1 \cdot 4 \cdot -13 = -52. \] 2. Multiply the denominators: \[ 5 \cdot 5 \cdot 8 = 200. \] So, we have: \[ \frac{-52}{200}. \] Next, we simplify the fraction. The greatest common divisor of 52 and 200 is 4: \[ \frac{-52 \div 4}{200 \div 4} = \frac{-13}{50}. \] Therefore, the final answer in simplest form is: \[ \boxed{-\frac{13}{50}}. \]