The limit of the expression $\lim_{{x \to 0}} \frac{{\sin(3x) + \sin(2x)}}{{5x}}$ is $1$.

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Here are some related questions:

1. How do you find limits involving trigonometric functions?
2. What is L'Hôpital's rule, and how can it be applied to limits like this?
3. How does the small-angle approximation for sine function help in limit problems?
4. Can the limit of a sum be split into individual limits?
5. How would the limit change if we had $\cos(3x)$ instead of $\sin(3x)$?

Tip: The small-angle approximation $\sin(x) \approx x$ for small values of $x$ is often useful in limit problems.