Let's break this down step by step:

Expression:

$5 \sqrt{75} + \sqrt{27} - \sqrt{50}$

We begin by simplifying each square root term:

1. Simplifying $\sqrt{75}$:

$\sqrt{75} = \sqrt{25 \times 3} = \sqrt{25} \times \sqrt{3} = 5\sqrt{3}$

Thus, $5 \sqrt{75} = 5 \times 5\sqrt{3} = 25\sqrt{3}$.

2. Simplifying $\sqrt{27}$:

$\sqrt{27} = \sqrt{9 \times 3} = \sqrt{9} \times \sqrt{3} = 3\sqrt{3}$

3. Simplifying $\sqrt{50}$:

$\sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2} = 5\sqrt{2}$

Now, substitute these simplified values back into the original expression:

$25 \sqrt{3} + 3 \sqrt{3} - 5 \sqrt{2}$

Combine like terms:

$(25 \sqrt{3} + 3 \sqrt{3}) = 28 \sqrt{3}$

So, the expression becomes:

$28 \sqrt{3} - 5 \sqrt{2}$

Final Simplified Expression:

$28 \sqrt{3} - 5 \sqrt{2}$

This is the simplest form of the given expression.

Do you need more details on any step?

Here are some follow-up questions:

1. How do you simplify square roots with prime factors?
2. Can you simplify expressions with multiple square roots further?
3. What is the difference between rationalizing and simplifying square roots?
4. How do you combine terms with square roots?
5. How do square roots apply in geometry?

Tip: Always factor the numbers under the square root to find perfect squares that simplify easily!