If I am measuring a length with a micrometer I might make 5 measurements and average.
if I have a box of 100 chips, 90 red and 10 blue a sample of 5 is pretty useless.
When making electrical measurements the sample size is determined by the noise parameters. and the noise is not always Gaussian and stationary, parameters may vary with time.
http://en.wikipedia.org/wiki/Signal_averaging
There is no magic '5'.
Average, yes. Standard deviation, doesn't mean much.
It all depends on the situation. My first major project was setting up a manufacturing defect reduction and SPC program.
Once the manufacturing systemic errors were minimized a change in mean or SD in manufacturing failure rates would generally be traceable to something changing.
http://en.wikipedia.org/wiki/Control_chart
if I am making measurements and the sd seems large I’ll take a look and see if there is a reducible cause.
If you are sampling some parameter from a population of widgets, like the weight, the sd is the estimate of the population variation. 6 Sigma. The confidence level is error estimate of the population estimate.
The mean without a 6 sigma estimate is useless. You need both when making a statistical decision.