Prior or posterior to looking for sources and failing to find one? If the latter, why?

Neither the thought nor the expression sound like Churchill, and Google didn't find a source. A more assiduous search (i.e. going through the first four pages of results instead of the first two) turns up this, a dustbin of unsourced quotations on the Wikipedia talk page for Churchill. At this point I think it pretty clear he never said it.

ETA: Here and here a Churchill historian who has published a book of Churchill quotations asserts he never said it, and gives some sourced quotations of some things he did say about democracy. They are completely inconsistent with the "five minute conversation" quote. I think that puts sufficient nails in the coffin.