Use the Distributive Property to prove that these algebraic expressions are equivalent. Explain your answer in one sentence for each expression and show your work.

To prove that the two expressions are equivalent using the Distributive Property, we will first simplify each expression step by step.

**Expression 1: \((x - 5)(x + 3)\)**

We will apply the Distributive Property (FOIL method) to multiply the two binomials:

1. First: \(x \cdot x = x^2\)
2. Outer: \(x \cdot 3 = 3x\)
3. Inner: \(-5 \cdot x = -5x\)
4. Last: \(-5 \cdot 3 = -15\)

Now, combine the like terms:

\[
(x - 5)(x + 3) = x^2 + 3x - 5x - 15 = x^2 - 2x - 15
\]

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**Expression 2: \(2x^2 - x^2 - 2x - 20 + 5\)**

Now, simplify this expression by combining like terms:

1. Combine \(2x^2 - x^2\):
\[
2x^2 - x^2 = x^2
\]
2. Next, combine the constants \(-20 + 5\):
\[
-20 + 5 = -15
\]

Putting it all together, we have:

\[
2x^2 - x^2 - 2x - 20 + 5 = x^2 - 2x - 15
\]

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**Conclusion:**

After simplifying both expressions, we find that:

- Expression 1 simplifies to \(x^2 - 2x - 15\).
- Expression 2 simplifies to \(x^2 - 2x - 15\).

Since both expressions result in the same polynomial, we conclude that the expressions are equivalent.