5 Points uniformly placed on a sphere
Solution 1:
The answer depends on what you mean by "uniform". One way of doing this is to minimize the "energy" the system would have if each of the points was a charged particle. This "Thomson's Problem" is quite a famous problem in global minimum finding algorithms.
The answer in this case for $n=5$ would be:
Two points on the poles, and three as an equilateral triangle on the equator.
More answers for other values of $n$ can be found here.