Giải phương trình sau \( \tan 5x + \cot \left( {x + \frac{ \pi }{2}} \right) = 0 \)?
A.\(\left[ \begin{array}{l}x = k\pi \\x = \frac{\pi }{4} + \frac{{k\pi }}{2}\end{array} \right.\,\,\,(k \in \mathbb{Z}).\)
B.\(x = \frac{\pi }{2} + k\pi ;k \in \mathbb{Z}.\)
C.\(x = \frac{\pi }{3} + k\pi ;k \in \mathbb{Z}.\)
D.\(x = \frac{{k\pi }}{4};k \in \mathbb{Z}.\)