1. **State the problem:** Find the median of the values $\frac{4}{3}$, $-2 \frac{1}{3}$, $1 \frac{4}{5}$, $-1 \frac{3}{5}$, and $-\frac{5}{3}$.\n\n2. **Convert all mixed numbers to improper fractions:**\n- $-2 \frac{1}{3} = -\left(2 + \frac{1}{3}\right) = -\frac{7}{3}$\n- $1 \frac{4}{5} = 1 + \frac{4}{5} = \frac{9}{5}$\n- $-1 \frac{3}{5} = -\left(1 + \frac{3}{5}\right) = -\frac{8}{5}$\n\n3. **List all values as improper fractions:**\n- $\frac{4}{3}$\n- $-\frac{7}{3}$\n- $\frac{9}{5}$\n- $-\frac{8}{5}$\n- $-\frac{5}{3}$\n\n4. **Convert all fractions to decimals for easier comparison:**\n- $\frac{4}{3} \approx 1.333$\n- $-\frac{7}{3} \approx -2.333$\n- $\frac{9}{5} = 1.8$\n- $-\frac{8}{5} = -1.6$\n- $-\frac{5}{3} \approx -1.666$\n\n5. **Order the values from smallest to largest:**\n$$-2.333, -1.666, -1.6, 1.333, 1.8$$\n\n6. **Identify the median:** The median is the middle value in the ordered list. Here, the middle value is $-1.6$, which corresponds to $-\frac{8}{5}$.\n\n**Final answer:** The median is $-\frac{8}{5}$.