1. **State the problem:** Simplify the quadratic expression $x^2 - 10x + 25$. 2. **Recall the formula:** A perfect square trinomial has the form $a^2 - 2ab + b^2 = (a - b)^2$. 3. **Identify terms:** Here, $x^2$ is $a^2$ with $a = x$, and $25$ is $b^2$ with $b = 5$. 4. **Check the middle term:** The middle term is $-10x$, which should be $-2ab = -2 \times x \times 5 = -10x$, matching perfectly. 5. **Rewrite the expression:** Using the perfect square trinomial formula, we get $$x^2 - 10x + 25 = (x - 5)^2$$ 6. **Final answer:** The expression simplifies to **$(x - 5)^2$**.