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To solve this problem, we need to simplify the given expression by dividing the coefficients and using the rules of exponents.

The expression is:

\[
\frac{-3x^{-2}y^3z^5}{-15x^{-4}y^6z^{-5}}
\]

### Step-by-Step Simplification:

1. **Simplify the Coefficients:**
   \[
   \frac{-3}{-15} = \frac{1}{5}
   \]

2. **Apply the Rules of Exponents:**

   When dividing like bases, subtract the exponents:

   - For \(x\):  
     \[
     x^{-2} \div x^{-4} = x^{-2 - (-4)} = x^{-2 + 4} = x^2
     \]

   - For \(y\):  
     \[
     y^3 \div y^6 = y^{3 - 6} = y^{-3}
     \]

   - For \(z\):  
     \[
     z^5 \div z^{-5} = z^{5 - (-5)} = z^{5 + 5} = z^{10}
     \]

3. **Combine the Simplified Terms:**

   The simplified expression is:

   \[
   \frac{1}{5} \cdot x^2 \cdot y^{-3} \cdot z^{10}
   \]

   Which can be written as:

   \[
   \frac{x^2 z^{10}}{5 y^3}
   \]

   However, since we are asked to use negative exponents and not to place any variables in the denominator, we rewrite it as:

   \[
   \frac{1}{5} x^2 y^{-3} z^{10}
   \]

### Final Answer:

\[
\frac{1}{5} x^2 y^{-3} z^{10}
\]

Would you like more details on any specific step, or do you have any questions?

### Related Questions:

1. How do you handle negative exponents when simplifying expressions?
2. What are the rules for multiplying and dividing exponents with the same base?
3. How can you express a fraction in a single line using negative exponents?
4. What happens to a term when its exponent is zero?
5. How do you convert an expression with negative exponents to one without?

**Tip:** Remember that any number or variable raised to the power of zero is equal to 1.

Simplify the expression \(\frac{-3x^{-2}y^3z^5}{-15x^{-4}y^6z^{-5}}\) with negative exponents as needed.

Learn how to simplify the algebraic fraction \(\frac{-3x^{-2}y^3z^5}{-15x^{-4}y^6z^{-5}}\) by applying exponent rules. This problem covers key algebraic concepts such as exponent division and simplifying fractions.

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