All depends on how anal you want to be
I tend to tell guys to familiarize themselves with the concepts of Confidence Interval and Confidence Level. There are on-line calculators for these two concepts, but the kicker is you typically need a solid SD and mean (which you won't have from 5 shots). Personally, I wouldn't run any calc's until I have ~40 - 50 rounds...but more is better.
If you want to only shoot a 5-shot group, I would use the median instead of the average, and completely ignore SD & ES 'reporting'.
To me, there is a direct analogy between group sizes and statistical measures. 3 shots groups will always be better than a 5 shot, and 5 shot better than 10 shot, etc. Pictures of 3 shot groups are only really good for posting pictures on-line. Similarly, 5 or 10 data points are only good for 'reporting' small SD or ES on the internet.
I'm not saying this to disparage anyone. I'm just saying that using bad numbers will cause you to chase errors in the wrong places down the line. For example, if you think you have a 0.25 MOA gun because of one 3-shot group, you may look in all the wrong places once you start seeing 0.75 or 1.0 MOA groups....maybe you just have a 1 MOA gun and don't know it.