Solve for \( x \). \[ -\frac{2}{x-5}=-\frac{8}{5 x-25}+1 \] If there is more than one solution, separate them with commas. If there is no solution, click on "No solution". \( x=\square \)

To solve the equation \[ -\frac{2}{x-5} = -\frac{8}{5x-25} + 1, \] first, notice that \(5x - 25\) can be factored as \(5(x - 5)\). Thus, we can rewrite the equation as: \[ -\frac{2}{x-5} = -\frac{8}{5(x-5)} + 1. \] Now, let's find a common denominator for the left side: \[ -\frac{2}{x-5} = -\frac{8}{5(x-5)} + 1. \] Multiply both sides by \(5(x - 5)\) to eliminate the denominators: \[ -10 = -8 + 5(x - 5). \] Expand the right side: \[ -10 = -8 + 5x - 25. \] Combine like terms: \[ -10 = 5x - 33. \] Add 33 to both sides: \[ 23 = 5x. \] Now, divide by 5: \[ x = \frac{23}{5}. \] Thus, the solution is \[ x = \frac{23}{5}. \] So, the answer is: \( x = \frac{23}{5} \)