To simplify the expression \(5\sqrt{27x} - \sqrt{75x}\), follow these steps:

1. **Simplify each square root separately:**

   - \(\sqrt{27x}\) can be simplified as follows:
     \[
     \sqrt{27x} = \sqrt{9 \cdot 3 \cdot x} = \sqrt{9} \cdot \sqrt{3} \cdot \sqrt{x} = 3\sqrt{3x}
     \]
     So, \(5\sqrt{27x} = 5 \times 3\sqrt{3x} = 15\sqrt{3x}\).

   - \(\sqrt{75x}\) can be simplified as follows:
     \[
     \sqrt{75x} = \sqrt{25 \cdot 3 \cdot x} = \sqrt{25} \cdot \sqrt{3} \cdot \sqrt{x} = 5\sqrt{3x}
     \]

2. **Subtract the simplified expressions:**

   \[
   15\sqrt{3x} - 5\sqrt{3x}
   \]

   This simplifies further as:
   \[
   (15 - 5)\sqrt{3x} = 10\sqrt{3x}
   \]

### Final Answer:
\[
5\sqrt{27x} - \sqrt{75x} = 10\sqrt{3x}
\]

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Here are 5 related questions:

1. How do you simplify \(4\sqrt{18x} + 2\sqrt{8x}\)?
2. What is the simplified form of \(\sqrt{50x} + 2\sqrt{32x}\)?
3. How do you add or subtract square root expressions like \(\sqrt{20x} - \sqrt{5x}\)?
4. What are the steps to simplify \(\sqrt{45x^2} + \sqrt{20x^2}\)?
5. How do you factor out common square roots from an expression like \(3\sqrt{12x} - 2\sqrt{3x}\)?

**Tip:** Always try to factor out the greatest common square factor from under the square root to simplify expressions easily.

Learn how to simplify the expression 5√(27x) - √(75x) with detailed step-by-step instructions. This problem involves simplifying square roots and is suitable for high school students studying algebra.

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