I have a sample of 5 numbers from known interval [0, 10]. Is 5 numbers is enough to make some conclusions about whether these numbers are drawn from uniform distribution or not?
To test $U(0,10)$ with $n=5$?
Not with much reliability, unless it's extremely nonuniform.
If you're expecting U-shaped alternatives, you might consider say an Anderson-Darling test, (it usually shows up well in power studies, so it's a good one to keep in mind more generally) -- but the power at $n=5$ is going to be quite low.
It's substantially more powerful than the Kolmogorov-Smirnov test on U-shaped alternatives.
With hill-shaped alternatives (like a beta(3,3), say), at n=5 the Anderson-Darling is very biased (i.e. has much less than $\alpha$ probability to reject), so it's not a great choice there, and the Kolmogorov-Smirnov test does better (though it, too, is biased - which means you have more power against a beta(3,3) by rolling a 20 sided die and rejecting when it comes up with a '1').
Here's an idea of how serious the bias problem is at n=5 (here I used a significance level of 10%, since $n$ is so small):
With a skew alternative that "piles up" probability at one end (such as a beta(2,1)), the power of the two tests is reasonable - somewhat like the power for the U-shape case, but the power of the two is more similar.
With those problems in mind, here are some followup questions:
Why are you testing uniformity?
Do you have any sense of likely alternatives?
What are the relative costs of the two types of error?
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