Splitting equilateral triangle into 5 equal parts
The answer is "yes", it is possible to divide equilateral triangle into $5$ equal parts, see the picture below which comes from here: https://ru-math.livejournal.com/831851.html
You might want to look at:
http://www.michaelbeeson.com/research/papers/TriangleTiling1.pdf
and the references given there.