Paul: it's more of a fifth date kinda revelation.
Paul: So you still think you, um... might want that fifth date?
Monica: (pause)...Yeah. Yeah, I do.
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Well I found those words here...
Is that where you saw them?
... but I have never actually seen this episode of Friends. So I'm responding to the words with only a little more context than you provided.
I think that when Paul says that it's more a fifth date kind of revelation, he's considering whether to tell her something surprisingly intimate, considering that they do not know each other well. Then, after telling her, he asks whether she would still like to date him. But he asks whether she "might want that fifth date" so that, if she is not sure whether she does want that fifth date, she will answer "yes." Her yes answer would then mean "Yes, I might want that fifth date. I'm not sure whether I do."
"I might" means "Maybe I will."