Hmm, I wonder if this is a good example to highlight differences between philosophies. I expect most people would take pretty much the same approach here, no matter what their philosophy. First, find out why the 5-year-old wants to stay in the monkey area. Because she thinks it's too cold outside? Because she really likes watching the monkeys? Because she's tired and doesn't want to walk anymore?
If it's too cold for the jacket she's wearing, I'd try to find a solution for that. Is there a place we could eat lunch inside? Even if everyone else would rather eat outside, it doesn't make sense if there's someone who isn't dressed for it. If the rest of the group feels really strongly about eating outside, maybe my DD and I could eat inside and then meet up with them afterwards. Or maybe a little activity would warm my DD up enough for her to enjoy being outside. Maybe I'd suggest playing an outdoor running game for 5 or 10 minutes and then see how she felt about the picnic lunch. I might suggest the game as motivation to leave the monkey area, or I might get her out by saying we could eat lunch in a warm place inside and then once we were outside, see if I could get her interested in the game and then see if running around had made her change her mind about eating outside. Or maybe I'd let her wear my coat over hers during the picnic. Being cold for a bit might be better than letting her get so miserable that it ruined the outing for her and for the rest of the group.
If she had a different reason for not wanting to leave (like she wanted to spend more time watching the monkeys), I'd try to think of something that would give her a motivation for leaving. Maybe I'd suggest that I could buy her some snack she liked or something from the gift shop. Maybe I'd talk about some other animal or area of the zoo I thought she'd really be interested in.
What I would really try not to do would be to make her leave. It might get her out faster, but then she'd be in a terrible mood and getting her out of that mood, or waiting for her to get over it, would probably take a lot longer than it would have taken to come up with something that would make her willing to leave. Maybe she'd end up so unhappy or angry that we'd just have to go home. If nothing else was working, before resorting to carrying her out or walking out without her (so she would have to follow or be left alone), I'd probably try to make a deal with her. If she'll do what I want - leave the monkey area - is there something I can do in return? I'd see if she had a suggestion and if she couldn't come up with a reasonable one, I'd offer some that I would be okay with (buy her a candy bar? let her watch a video this evening? have an hour of special "mom and DD" time the next day?)
I suppose the "making a deal" idea is the one other people might be most likely to disagree with. It's something I've done with my kids, and it does sometimes lead to a kid saying, "What can I have if I do X?" or "I won't do X unless you do Y." But if it's not something I think it's appropriate to make a deal over, I won't. Toothbrushing, for instance, just has to happen and I'm not going to agree to give any kind of bribe or reward for it. Making a deal is a reasonable approach that adults often use when they want different things, and I think it's okay to teach kids to use that approach, either with each other or with adults.