1. **State the problem:** Solve the equation $5(X-5)^2=25$ for $X$. 2. **Isolate the squared term:** Divide both sides by 5 to simplify. $$5\cancel{(X-5)^2} \div 5 = 25 \div 5$$ which simplifies to $$(X-5)^2 = 5$$ 3. **Take the square root of both sides:** Remember to consider both positive and negative roots. $$X-5 = \pm \sqrt{5}$$ 4. **Solve for $X$:** Add 5 to both sides. $$X = 5 \pm \sqrt{5}$$ 5. **Final answer:** The solutions are $$X = 5 + \sqrt{5} \quad \text{or} \quad X = 5 - \sqrt{5}$$