After doing a bit of research I have concluded the following:
1. There are probably 50 sites promoting the 5 step method to every 1
debunking it.
2. Francis Bacon promoted inductive reasoning vs deductive, and probably
never codified a 5 step method, although he is sometimes credited for it. I
even came across a term paper purveyor with a sample paper claiming this!
3. In 1999 one article in The Physics Teacher said that the 5 step method
is anathema to physicists. This is not new news.
4. Hewett includes it in his text and then afterwards says that this is a
simplistic method which does not reflect what real scientists do. He
probably included it to make the book saleable. So teachers teach it even
though the author disavows it.
But I came across an interesting web site where it is debunked and where
some interesting ideas were brought up as to where it came from. So it
probably was not invented by biologists, although it may be embraced by
them.