5 months old might be a bit young for molting, though not impossible, more than likely improbable, Molting is the loss of old feathers replaced by new feathers it can happen in as few as 2-3 weeks or can last over a period of months and usually occurs when a bird is about a year old give or take a few months, without seeing the feet I can't be sure of what your describing as flakey
In one of my books it said that if beaks and feet peel when not in moult (I agree with Bobby, this isn't likely) can mean either a Vit E deficiency (apparently a relatively common cause) or the air is too dry where you live (biggest cause). If it's really dry and hot, then their uncovered bits will dry out just like our uncovered bits lol. Apparently air humidifyers work a treat for this. I'd suggest if neither of these are a problem - vet time, just to be safe.
I will never have this problem as I live in the UK lol. Ho hum.