Q:

Puzzle pieces, each in contact with 5 others

You are asked to create puzzle pieces by joining together identical squares. This needs to be done such that the puzzle pieces can be arranged in a pattern with each piece being in contact with exactly 5 others. In terms of number of starting squares, how low can you go?

Background and further clarification 

Here we saw that 64 identical squares can be joined into puzzle pieces which can subsequently be grouped together in a square such that each piece is in contact with exactly 5 other pieces.
Here we saw that 42 identical squares can be joined into puzzle pieces which can subsequently be grouped together in a rectangle such that each piece is in contact with exactly 5 other pieces. 
Now we are getting rid of the requirement to group the puzzle pieces into a specific shape: any shape will do!
We still require two squares being 'joined' or two puzzle pieces being 'in contact' to mean that both share a finite portion of their perimeter. 
Also, the joining of the squares into puzzle pieces as well as the grouping of these pieces, is to be done within a plane and without creating any overlap. In other words, there should be no loss of total area covered: the resulting total puzzle needs to cover an area identical to that of the sum of the squares used.

So far this puzzle has seen zero attempts towards a solution. As long as progress is lacking, every one or two days I will publish a hint. 
The first hint:

 In contrast to the 64 square and 42 square solutions, the solution sought does deploy single square puzzle pieces.

A:

assuming a staggered grid isn't illegal because the expected solution includes single squares
27 squares.

A:

Upon request, here is the solution I had in mind:

This solution is in essence the same as arbitrary's, as it is based on the same icosahedral graph (the smallest planar regular graph with vertex connectivity 5):

