Choice C is the correct answer. This expression fits the Difference of Squares pattern: $a^2 - b^2 = (a - b)(a + b)$.

1. Identify $a$ and $b$: $x^2$ is $(x)^2$ and $25$ is $(5)^2$.
2. Apply the formula: $(x - 5)(x + 5)$.

This is a crucial pattern to recognize instantly on the SAT.

Choice A is incorrect because $(x-5)^2 = x^2 - 10x + 25$, which has a middle term. Choice B is incorrect because $(x+5)^2 = x^2 + 10x + 25$, which also has a middle term. Choice D is incorrect because expanding it gives $x^2 - 24x - 25$.