Find the domain of the function. \[ f(x)=\sqrt{5 x-25} \] The domain is \( \square \). (Type your answer in interval notation.)

To determine the domain of the function \( f(x) = \sqrt{5x - 25} \), we need to ensure that the expression inside the square root is non-negative. Thus, we set up the inequality: \[ 5x - 25 \geq 0. \] Solving for \( x \), we first add 25 to both sides: \[ 5x \geq 25. \] Next, we divide both sides by 5: \[ x \geq 5. \] Therefore, the domain of the function in interval notation is: \[ [5, \infty). \] To check if any common mistakes were made, it's vital to remember that the expression under a square root must not be negative. This is a common pitfall when working with roots that can lead to mistakes in setting up the inequality. So always ensure the expression in the radical is greater than or equal to zero!