What is the man saying at 5:00 ? I'm not sure, it sounds somehow like: 僕の永遠になって下さい。boku no eien ni natte kudasai. And isn't it more polite to use 君 (kimi) instead of あなた (anata)?
"He says: 僕の親に会ってください (Please meet my parents) which is basically a marriage proposal. あなた (anata) is more polite than 君 (kimi). Earlier in this episode he uses 君 (kimi) with someone else's wife and people look at him very strange because it's too casual."