The expression $(10^{-3})^{-5}$ can be simplified by using the property of exponents $(a^m)^n = a^{m \cdot n}$.

Let's simplify:

$(10^{-3})^{-5} = 10^{-3 \times -5} = 10^{15}$

Thus, $(10^{-3})^{-5} = 10^{15}$.

Would you like any further details or have any questions?

Here are 5 related questions to explore:

1. How do you simplify $(a^{-2})^{-3}$?
2. What is the value of $(2^{-4})^2$?
3. How do you apply the power of a power rule in exponents?
4. What is the value of $10^3 \times 10^2$?
5. How do you simplify $\left(\frac{10}{5}\right)^3$?

Tip: When raising a power to another power, multiply the exponents!