How to average best 3 of 5 scores with entries missing

I'm new here so I'm very sorry if this has been posted elsewhere.

I am needing to track scores and instead of doing a straight average of all scores, I want to average the best 3 out of the last 5 scores posted.

In my example, you can see that I have 7 people who have posted scores. I have also added the average of these scores in the "TOTAL AVE" column. You can see, that since not everyone posted a score every week, there are weeks without scores. So I am looking to use the last 5 scores posted and average the best 3 of them for each person.

Can anyone help me out with this?

I thank you all in advance for your assistance.