Factor x^2 - 25 completely.

Step 1: Recognize x^2 - 25 as a difference of squares:
x^2 - 5^2

Use the difference-of-squares identity:
a^2 - b^2 = (a - b)(a + b)

Step 2: Apply the formula
x^2 - 25 = (x - 5)(x + 5)

Both factors are linear, so the expression is completely factored.

Step 3: Check by multiplying
(x - 5)(x + 5) = x^2 + 5x - 5x - 25

The middle terms cancel: 
x^2 - 25