Show a list where min. number > 5 in worksheet forumula

I'm trying to return a list with a given criteria

My current data looks like

      A        B1   Anna       4  2   Brad       63   Claire     24   Dan        54   Evie       2

I want to select those with a "score" of 4 or less, and sort them in order!

As such, I'd love to see the result like (note the different columns)

      D        E1    Claire    22    Evie      2  3    Anna      4

I do not want to use pivot tables. I'm trying to learn what is actually possible with worksheet functions.

Is what I want to achieve possible?

The rest of this post doesn't work - I just wanted to prove that I had tried

I've had a go at the first part (to get column D working) which is to match those with a score of less than 5

=INDEX($A$1:$A$4, SMALL(IF($B$1:$B$4>4,ROW($B$1:$B$1)), ROW()))

This fails because Small appears to return the item that matches small, as such, my result won't include both Claire and Evie as they both have a score of 2