To solve the given problem, let's simplify the expression step-by-step:

The expression is: $\frac{16r^3 t z^5}{-4 r t^3 z^2}$

1. Simplify the Coefficients: $\frac{16}{-4} = -4$

2. Simplify the Powers of $r$: $\frac{r^3}{r} = r^{3-1} = r^2$

3. Simplify the Powers of $t$: $\frac{t}{t^3} = t^{1-3} = t^{-2} = \frac{1}{t^2}$

4. Simplify the Powers of $z$: $\frac{z^5}{z^2} = z^{5-2} = z^3$

Combining these, we get: $-4 \cdot r^2 \cdot \frac{1}{t^2} \cdot z^3 = -\frac{4 r^2 z^3}{t^2}$

Thus, the answer is: $\text{Option E: } -\frac{4 r^2 z^3}{t^2}$

Let me know if you would like a more detailed explanation or have any questions.

Here are some related questions you might find interesting:

1. How would the result change if the exponents of $r$, $t$, or $z$ were different?
2. What happens if any of the variables are zero?
3. How does simplifying powers work in other contexts?
4. Can you apply these simplification steps to other fraction problems?
5. Why does the negative sign affect the overall answer?

Tip: Always start by simplifying constants and common factors to make complex expressions easier to manage.