The expression provided in the image is:

$\frac{5x(x - y)}{x^3(y - x)}$

Let's simplify this step by step.

Step 1: Factor out common terms

Notice that $(y - x)$ can be rewritten as $-(x - y)$. Using this, we rewrite the denominator:

$\frac{5x(x - y)}{x^3(-(x - y))} = \frac{5x(x - y)}{-x^3(x - y)}$

Step 2: Cancel out the common factor $(x - y)$

Assuming $x \neq y$ to avoid division by zero, we can cancel out $(x - y)$ from the numerator and denominator:

$\frac{5x}{-x^3}$

Step 3: Simplify the remaining expression

Now simplify the fraction:

$\frac{5x}{-x^3} = -\frac{5}{x^2}$

Final Answer:

The simplified form of the given expression is:

$-\frac{5}{x^2}$

Would you like more details or have any questions?

Here are five questions related to this expression:

1. How does rewriting $y - x$ as $-(x - y)$ simplify the problem?
2. Why is it important to specify that $x \neq y$?
3. What happens if $x = y$?
4. How would the problem change if the denominator had an additional term like $x^4$?
5. Can this simplified expression be used to find limits as $x \to 0$?

Tip: Always check for terms that can be factored or canceled to simplify expressions quickly!