We are given the following expression:

$\frac{5 - 2 \sin^2 \theta \cos^2 \theta}{\sin^2 \theta \cos^2 \theta}$

Let's break it down step by step:

1. Separate the terms in the numerator: The numerator has two terms, $5$ and $-2 \sin^2 \theta \cos^2 \theta$. We can split the fraction accordingly: $\frac{5}{\sin^2 \theta \cos^2 \theta} - \frac{2 \sin^2 \theta \cos^2 \theta}{\sin^2 \theta \cos^2 \theta}$

2. Simplify the second term: The second term simplifies directly because the denominator is the same as the numerator: $\frac{2 \sin^2 \theta \cos^2 \theta}{\sin^2 \theta \cos^2 \theta} = 2$

   So the expression becomes: $\frac{5}{\sin^2 \theta \cos^2 \theta} - 2$

3. Use a trigonometric identity: Recall that: $\sin^2 \theta \cos^2 \theta = \frac{1}{4} \sin^2 2\theta$ Using this identity, we rewrite the first term: $\frac{5}{\sin^2 \theta \cos^2 \theta} = \frac{5}{\frac{1}{4} \sin^2 2\theta} = \frac{20}{\sin^2 2\theta}$

4. Final simplified form: The expression simplifies to: $\frac{20}{\sin^2 2\theta} - 2$

Thus, the simplified form of the given expression is:

$\frac{20}{\sin^2 2\theta} - 2$

Would you like more details on any of these steps or have any questions?

Here are 5 related questions you might find interesting:

1. How do trigonometric identities simplify complex expressions?
2. What is the significance of double-angle identities in trigonometry?
3. How can trigonometric functions be used to solve real-world problems?
4. What are some common mistakes when working with trigonometric simplifications?
5. How does the Pythagorean identity help in simplifying trigonometric expressions?

Tip: Memorizing key trigonometric identities, such as double-angle and Pythagorean identities, can significantly speed up solving problems involving trigonometric functions.