$\lim _{x\to 0}\left(\sin\left(x\right)\cos\left(\frac{5}{x}\right)\right)$ Can I apply Sandwich Theorem to this limit?

Question

Actually the original question was the following

Determine whether the following limit exist?

$\lim _{x\to 0}\left(x^2\sin\left(\frac{2}{x}\right)+\sin\left(x\right)\cos\left(\frac{5}{x}\right)\right)$

I know I can apply Sandwich Theorem to the following limit

$\lim_{x\to 0}\left(x^2\sin\left(\frac{2}{x}\right)\right)$

but the second part of the function i am not sure, so please help me with this problem. Thank you.