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The distance is not a fixed or defined specification per-se. The distance is for the purpose of preventing muzzle blast from effecting the velocity readings.
Thus, you will find a great deal of practical flexibility in distance based on the cartridge being tested and the characteristics of the rifle (or pistol).
The number of shots "appropriate" is also flexible based on the information you seek to learn.
For instance; three shots is plenty if you are doing load development and simply want to know if you are "in the ball park yet".
Five shots - in my opinion - is the point where you begin to get sufficient data to make judgement regarding the quality (consistency) of the ammunition you are testing. More shots may be appropriate if diagnosing deviation. For instance, "is it consistent charge weight or crimp, or lack of crimp, or neck tension causing the deviation in velocity?" or you simply desire to minimize deviation and confirm success of failure in your efforts.
This is abbreviated. A lot more can be said on this topic, but I think that this is a pretty good snapshot of the basics . . . . hope it helps. A chronograph is a wonderfully useful tool whose value - particularly to a handloader - is most frequently underappreciated.
I'd rather be lucky than good, but I'd rather KNOW I'm good than HOPE to get lucky. 
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