If $pp$ and $qq$ vary inversely, this means that their product is constant. Mathematically, this relationship can be expressed as:

$pp \times qq = k$

where $k$ is a constant.

Given that $pp = 10$ when $qq = 16$, we can first find the value of $k$:

$10 \times 16 = 160$

So, $k = 160$.

Now, we are asked to determine $qq$ when $pp = 5$. Using the same inverse variation equation:

$5 \times qq = 160$

Solving for $qq$:

$qq = \frac{160}{5} = 32$

Thus, when $pp = 5$, $qq = 32$.

Would you like more details on inverse variation or how I derived this?

Here are 5 related questions to expand your understanding:

1. How does the concept of inverse variation apply to real-world problems?
2. What happens to $qq$ if $pp$ is doubled in an inverse relationship?
3. Can you explain how inverse variation differs from direct variation?
4. How do you solve for $pp$ given $qq$ and the constant $k$?
5. What would the graph of an inverse variation relationship look like?

Tip: When dealing with inverse variation, remember that as one quantity increases, the other decreases proportionally.