(1) $$ \frac{25^{-5} \cdot 15^{x+1}}{3^{x} \cdot 5^{-5}} $$ 2) $$ (3 m-2 n)(m+2 n-5) $$

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Simplify the expression by following steps:
- step0: Multiply the terms:
  $$\left(3m-2n\right)\left(m+2n-5\right)$$
- step1: Apply the distributive property:
  $$3m\times m+3m\times 2n-3m\times 5-2nm-2n\times 2n-\left(-2n\times 5\right)$$
- step2: Multiply the terms:
  $$3m^{2}+6mn-15m-2nm-4n^{2}-\left(-10n\right)$$
- step3: Remove the parentheses:
  $$3m^{2}+6mn-15m-2nm-4n^{2}+10n$$
- step4: Subtract the terms:
  $$3m^{2}+4mn-15m-4n^{2}+10n$$
Calculate or simplify the expression $$ \frac{25^{-5} \cdot 15^{x+1}}{3^{x} \cdot 5^{-5}} $$.
Simplify the expression by following steps:
- step0: Solution:
  $$\frac{25^{-5}\times 15^{x+1}}{3^{x}\times 5^{-5}}$$
- step1: Factor the expression:
  $$\frac{5^{-10}\times 15^{x+1}}{3^{x}\times 5^{-5}}$$
- step2: Reduce the fraction:
  $$\frac{15^{x+1}}{3^{x}\times 5^{5}}$$
- step3: Factor the expression:
  $$\frac{3^{x+1}\times 5^{x+1}}{3^{x}\times 5^{5}}$$
- step4: Reduce the fraction:
  $$3\times 5^{x-4}$$
Let's break down the solutions for both expressions step by step.

### 1) Simplifying $$ \frac{25^{-5} \cdot 15^{x+1}}{3^{x} \cdot 5^{-5}} $$

**Step 1: Rewrite the bases.**
- $$ 25 = 5^2 $$, so $$ 25^{-5} = (5^2)^{-5} = 5^{-10} $$.
- $$ 15 = 3 \cdot 5 $$, so $$ 15^{x+1} = (3 \cdot 5)^{x+1} = 3^{x+1} \cdot 5^{x+1} $$.

**Step 2: Substitute back into the expression.**
$$
\frac{5^{-10} \cdot (3^{x+1} \cdot 5^{x+1})}{3^{x} \cdot 5^{-5}} = \frac{3^{x+1} \cdot 5^{-10 + x + 1}}{3^{x} \cdot 5^{-5}}
$$

**Step 3: Simplify the powers of 5.**
$$
= \frac{3^{x+1}}{3^{x}} \cdot 5^{-10 + x + 1 + 5} = 3^{(x+1) - x} \cdot 5^{-4 + x} = 3^{1} \cdot 5^{x - 4}
$$

**Final Result:**
$$
3 \cdot 5^{x - 4}
$$

### 2) Expanding $$ (3 m-2 n)(m+2 n-5) $$

**Step 1: Use the distributive property (FOIL method).**
- First: $$ 3m \cdot m = 3m^2 $$
- Outer: $$ 3m \cdot 2n = 6mn $$
- Inner: $$ -2n \cdot m = -2mn $$
- Last: $$ -2n \cdot -5 = 10n $$

**Step 2: Combine like terms.**
$$
3m^2 + 6mn - 2mn + 10n = 3m^2 + (6mn - 2mn) + 10n = 3m^2 + 4mn + 10n
$$

**Final Result:**
$$
3m^2 + 4mn - 15m - 4n^2 + 10n
$$

### Summary of Results:
1) $$ \frac{25^{-5} \cdot 15^{x+1}}{3^{x} \cdot 5^{-5}} = 3 \cdot 5^{x - 4} $$

2) $$ (3 m-2 n)(m+2 n-5) = 3m^2 + 4mn - 15m - 4n^2 + 10n $$
1) $$ 3 \cdot 5^{x - 4} $$ 2) $$ 3m^2 + 4mn - 15m - 4n^2 + 10n $$

(1) \( \frac{25^{-5} \cdot 15^{x+1}}{3^{x} \cdot 5^{-5}} \) 2) \( (3 m-2 n)(m+2 n-5) \)

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