What is wrong with my solution to this trigonometric equation: $\sin x – 5\cos x = 0$?

\begin{align*} \sin x- 5\cos x & = 0\ \tan x\frac{\sin x}{\tan x}-5\frac{\sin x}{\tan x} & =0\ \sin x(\tan x- 5) & =0 \end{align*}
I think it has something to do with my writing $ \cos x$ as $ \frac{\sin x}{\tan x}$