Solve the equation for exact solutions over the interval $[0,2 \pi)$.
\[
5 \cot x+3=-2
\]

Select the correct choice below and, if necessary, fill in the answer box to com

Step 1 ：Subtract 3 from both sides of the equation: \(5\cot(x) + 3 - 3 = -2 - 3\), which simplifies to \(5\cot(x) = -5\)

Step 2 ：Divide both sides by 5 to solve for \(\cot(x)\): \(\cot(x) = -5/5\), which simplifies to \(\cot(x) = -1\)

Step 3 ：Rewrite the equation as \(\tan(x) = -1\) since the cotangent function is the reciprocal of the tangent function

Step 4 ：The solutions to this equation in the interval [0, 2π) are \(x = \frac{\pi}{4} + n\pi\), where n is an integer

Step 5 ：Since \(\cot(x)\) is negative, we only consider the solutions in the second and fourth quadrants, which are \(x = \frac{3\pi}{4}, \frac{7\pi}{4}\)

Step 6 ：\(\boxed{x = \frac{3\pi}{4}, \frac{7\pi}{4}}\) are the exact solutions to the equation over the interval [0, 2π)