1. **State the problem:** Simplify the expression $\sqrt{72} + \sqrt{50} - \sqrt{25}$.\n\n2. **Recall the formula and rules:** The square root of a product can be expressed as the product of square roots: $$\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$$. Also, simplify square roots by factoring out perfect squares.\n\n3. **Simplify each term:**\n- $\sqrt{72} = \sqrt{36 \times 2} = \sqrt{36} \times \sqrt{2} = 6\sqrt{2}$\n- $\sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2} = 5\sqrt{2}$\n- $\sqrt{25} = 5$\n\n4. **Substitute back into the expression:**\n$$6\sqrt{2} + 5\sqrt{2} - 5$$\n\n5. **Combine like terms:**\n$$ (6\sqrt{2} + 5\sqrt{2}) - 5 = 11\sqrt{2} - 5$$\n\n6. **Final answer:**\n$$11\sqrt{2} - 5$$