my gut feeling is, what an unusually enlightened homeopath. ( while 3-5 weeks struck me initially as a lot...more on that in a minute) I stumbled onto water fasting after doing a ten day retreat a few years back. ( the retreat set me up for a shift in the paradigm!) I would have believed people.. die too, before this, :-) even though I had once done a three day water fast as a teenager, to quit smoking, and had actually started to feel "too good".
I started reading some of the literature in the soil and health library--a wonderful resource. Shelton and Purinton are two favorites around here. You can find lots of water fasting manuals at Soil and Health--or use the search feature on this forum, to come up with some links. Chris B used to always post excerpts from Shelton's work, in answer to the questions of newcomers--so you could search his posts also, for lots of good information.
I was 'diagnosed' as hypoglycemic when I was a child, and used to get headaches daily. I also had nephritis as a child--and I was a bit concerned and confused initially about water fasting. I had some hormone issues too, various aches and pains and I can't remember what all. After doing the aforesaid reading, (along with a story by a doctor who cured himself of life-threatening illness--forget his name, sorry!)I felt completely confident that water fasting was exactly what I wanted to do. My first WF was 29 days. There was no way I could go to a retreat centre to do it, nor did I have any "supervision" (love that word) other than the larger (super- )vision of such as ChrisB and a few others, on this site.
Long story shortened: I no longer have any hypoglycemic issues. I eat less and feel happier. if I want to eat more, I do--but have a new appreciation for nutrient-dense food in small portions. Normally, I feel best on one meal a day now, with maybe juice as a second 'meal'. Since that first WF I've done several more. A 21 day, and then some shorter ones. It's a life-changing mind-expanding experience. 5 weeks sounds like quite a challenge, esp.with children. But I think 21 days is very doable.
Can't speak to the concern with the "eating disorder", though it may well be -or so I intuit- that a water fast undertaken with care and true understanding of the process, and not fixated on 'weight loss' can sort out a lot of the issues contributing to any such 'disorder'. It sounds as though you are very reflective and open, and I think that's a real plus. I'd encourage lots of reading from the soil and health library. There comes a place where you just know it's the right thing, and it all clicks.
Or so it did for me. The homeopath sounds like a very good support person, also.
best, Chiron
* re "true understanding of the process", I've seen lots of people jump into the water fast without having done the reading that would satisfy their concerns orhidden fears--and then they second guess the whole thing, and sabotage it, with adding things to it. There is a mantra here that really means seomthing, and is not just empty words. "water only, according to thirst". I have so enjoyed and benefited from reading f the old fasting masters' stories, and that 'mantra' has proved itself as the real thing, ( not just an empty slogan) again and again.