I need to evaluate this limit:

$$
\lim\_{x \to 0 }\frac{2x-\sin(3x)}{4x-\sin(5x)}
$$

I did: $$\frac{2x}{4x-\sin(5x)}-\frac{\sin(3x)3x}{(4x-\sin(5x))3x}$$

$$
\frac{2x}{4x-\sin(5x)}-\frac{3x}{4x-\sin(5x)}
$$

$$
\frac{-x}{4x-\sin(5x)}
$$

$$
\frac{-5x}{\sin(5x)(\frac{4x}{\sin(5x)}-1)\*5}
$$

$$
\frac{-1}{(\frac{4x}{\sin(5x)}-1)5} =\frac{1}{5}
$$

I know that I did wrong since the answer is 1..
What did I do wrong? How can you evaluate this limit?

Thanks! :)