My DD is 5.6 and she is allowed considerable freedom, but within strict guidelines.
When out and about at parks /shops/public places I tend to specifically state the area that she is allowed to roam off in, so she will go out of my sight - but she knows her limits and that if she breaks my trust she will not be allowed away from my side for the rest of the trip (although she has not done that for almost two years now).
In terms of strangers, my DD will happily talk to anyone - but she knows that some strangers are nice and others are not nice (she also knows all about the madeline mcann case and knows that some children do go off with strangers and are never seen again), but she also knows that even if she talks to someone she is not allowed outside her designated area and she will not go outside that (I know this because I have witnessed her refusing to go off with a well meaning adult who was trying to help her once).
In and around the house, she is allowed to ride the bike in front of the house and up and down the pavement (but is not allowed on the road) and again within a strict designated area. I do not stand outside and watch her, but observe occassionally and again know that she does not break her boundaries. In the house, again she is given a lot of freedom. She gets up of a weekend morning and makes her own breakfast (cereal, laid out on the table) and happily looks after herself. She also runs errands to neighbouring houses and to the postbox, but there are no major roads to cross.
So yes, I do give her lots of freedom, but it is also set within quite strict guidelines and she knows if she breaks them then she loses that trust. She is also a very sensible little girl so I can trust her. But I do also test her to see if I can trust her and the answer is usually yes. I think I would be less trusting of her little sister as she is more of a free spirit and less responsible in her character.