5. Which of the following is equivalent to \( x^{2}-25 \) ? A. \( x(x-25) \) B. \( (x-5)^{2} \) C. \( (x+5)(x-5) \) D. \( (x-25)^{2} \) E. \( \frac{(x+y)}{(x-y)} \)

To determine which of the options is equivalent to \( x^{2}-25 \), we can recognize that \( x^{2}-25 \) is a difference of squares. The difference of squares can be factored using the formula: \[ a^{2} - b^{2} = (a - b)(a + b) \] In this case, we can identify \( a = x \) and \( b = 5 \). Therefore, we can factor \( x^{2}-25 \) as follows: \[ x^{2} - 25 = (x - 5)(x + 5) \] Now, let's evaluate the options provided: A. \( x(x-25) \) - This does not match our factorization. B. \( (x-5)^{2} \) - This is not equivalent to our factorization. C. \( (x+5)(x-5) \) - This matches our factorization. D. \( (x-25)^{2} \) - This does not match our factorization. E. \( \frac{(x+y)}{(x-y)} \) - This is not relevant to our factorization. Thus, the correct answer is: **C. \( (x+5)(x-5) \)**.