Your debate (as with state v. private schools in general) seems quite polarised. In real life things are not that tidy.
Schools are seldom either 'wonderful' or 'terrible'. Presumably we would all have a cutoff point at which we would not send our child to a local school, but it might be helpful to explore what is driving those fears.
Personally, I would start to get a bit twitchy if my child had no like-minded kids to hang out with, and by 'like-minded' I don't mean white middle-class kids, but children who are compatible in terms of interests and personality. I would also be worried if the atmosphere at the school was so unruly as to be threatening and chaotic.
Apart from those extremes, the only way to make a decision is to invest time looking at different schools, what they have to offer and considering how they might suit your child's personality. You need to look at a lot of schools, as it is the differences that are revealing.
Most private schools have glitzy facilities; most urban schools will have groups of teenagers hanging around trying to look cool and threatening; most inner London primary schools will have lots of kids from tough estates and varied ethnic minority backgrounds, some of whom may not speak English. None of this in itself makes a good or bad school -- you need to look more deeply to make a good choice.
Personally, I'd have to be desperate to send my 8yo to boarding school. But you can't make this decision in principle for a 5 yo. You need to wait, find out about the child's personality and take a long hard look at the potentially available schools nearer the time.