There are infinitely many possible answers:
{5.8, 5.8, 5.8, 5.8, 6.8}
or {5.5, 6, 6.5, 6-a and 6+a} where a is any number less than or equal to 0.5
are two options.
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It is easy to prove that such a set of numbers cannot exist. If the median is -1 and the mean is different from the median, then there must be at least one number that is less than or equal to -1. Then, if the range is 6, the largest number can only be 5. If the largest number is 5 and the mean is 5, then all the numbers must be 5. That is not possible because there is at least one that is -1 or smaller.
1, 4, 10
Range: 5 Mean: 3
Yes.
4, 5, 5, 8, 8