Given that $\sin x = \frac{5}{2}$, this value is not valid because the sine function's range is limited to $-1 \leq \sin x \leq 1$. Since $\frac{5}{2} = 2.5$ is outside this range, it is impossible for $\sin x$ to equal $\frac{5}{2}$.

Could you double-check the value you provided for $\sin x$? It might be a typo or mistake. Feel free to provide the correct value, and I can help you find $\sin 2x$.

Would you like to proceed with another question or clarification? Here are five questions that can extend this topic:

1. How do we find the double-angle identity for sine?
2. What happens if $\sin x$ is larger than 1?
3. How do you calculate $\sin 2x$ using trigonometric identities?
4. What are the implications if $\sin x = \frac{5}{2}$ in a theoretical context?
5. Can the sine function have any other range in a different mathematical system?

Tip: The double-angle identity for sine is $\sin 2x = 2 \sin x \cos x$.