Scene five opens with tom reading the paper while Amanda and Laura clean the kitchen. Amanda is in usually form, nagging her son to comb his hair. Tom attempts to flee to the fire escape to smoke, but she begins complaining about how much money he spends on cigarettes. She tells him to imagine what he could do with the extra money, and suggests that he would have enough to take night classes. Tom bitterly responds that he would rather smoke.

At this point Tom briefly becomes the narrator again. He delivers a monologue about a place called Paradise Dance Hall that is across the ally from his family's apartment. He talks about the music and the lights emanating from the buildings, and about the carefree dancers who had no idea about the bombings in Guernica, and how they couldn't imagine that change was coming for them too.

After Tom's monologue Amanda joins him on the fire escape. Tom tells her that he has found a gentleman caller for Laura, and that he will be coming over for dinner the next night. Amanda is pleased that Tom as finally found someone, but worried that she wont be able to make the apartment presentable in time. Amanda has big plans for the event; she thinks she'll need a new floor lamp. She wants to polish her wedding silver, and put chintz covers on the furniture. She interrogates Tom about Laura's potential suitor, and seems quite concerned that he might be a drunkard. Tom assures her that the suitor, a young man named Jim O'Connor is not a heavy drinker. He tells her that he is a shipping clerk at the warehouse who makes 20 more dollars a month than Tom himself. He explains that while Jim is just average working he does go to night school, and is very ambitious.

Tom is nervous because he has not mentioned his sister to Jim. Amanda has bizarre confidence in her painfully shy daughter's ability to woo this potential suitor, but Tom is more realistic about the situation. Tom urges his mother to moderate her expectations, and points out that they can see Laura's beauty and excellent qualities because they know her intimately. But Tom points out that Laura is crippled (which infuriates his mother who says that word is not allowed in their house), and that she has some very odd interests (the old phonographs and the glass menagerie). Tom then leaves, as always, for "a movie."

Amanda's confidence is somewhat shaken by Tom's observations. She calls Laura out to the fire escape and asks her to make a wish for "good fortune" on the moon. As Laura does this, Amanda's eyes fill up with tears.

When the sixth seen opens Tom is again addressing the audience. He explains that he and Jim had gone to the same high school together, and that Jim had been the class hero. He had been the class president, a basketball star, and the lead in all of the yearly light operas. Six-years on his job is not much better than Tom's. Tom recalls how the other works at the warehouse hadn't initially liked him because he was aloof and odd, but that Jim had helped the other men accept him. Jim also notes that he has a private name for Jim: "Shakespeare" because he is always stealing away to write poetry.

Williams' stage directions indicate that Amanda has done an excellent job making the little apartment ready for the big event. Amanda stuffs Laura's bra with two powder puffs, and Laura is terribly abashed. Amanda, for her part, is wearing a girlish dress kept from her youth. The dress spurs memories of her youth, during which she spent all of her time going to parties and dancing. Amanda's wistful recollections end abruptly when she recounts meeting the father of her children.

When Laura hears the name of the gentlemen caller for the first time, she realizes that it might be the very same "Jim" she had a crush on in high school. She tells her mother that if it is the same Jim she will not be able to force herself to go to the table. The doorbell rings and Amanda attempts to get Laura to open the door, but she's terrified and insists that she cannot. Amanda is eventually able to pressure Laura to answer the door, and does so painfully awkward. Jim who, was very warm, is perplexed by her behavior. Tom explains that his sister is "terribly shy." Jim says that it's "nice to meet a shy girl these days."

While the men wait for the women to finish dinner, Jim talks about the self-improvement courses he has been taking at night. He encourages Tom to enroll in some night classes, but Tom is uninterested. Jim warns Tom that the supervisor at work has been unhappy with his work, and that he might find himself out of the job soon. Tom is indifferent, and tells Jim that he is planning on becoming merchant seamen. He reveals that he had not paid the electric bill that month, instead he had paid his dues to The Union of Merchant Seamen. He reveals that he plans to leave St. Louis soon, and that his family doesn't know about his plans. Jim is incredulous, but the men don't get a chance to discuss it further, because Amanda interrupts him.

Tom goes to fetch Laura for dinner, but she's too mortified to join them. The scene ends with Amanda, Tom, and Jim sitting down for dinner. The audience can also see Laura lying on a sofa in the living room trying not to cry.

When scene seven starts the three are just finishing dinner when the lights go out. Tom pretends not to know why the electric has gone off. Amanda suggests that he checks the fuse box, but Jim, know the truth of the situation, tells her that it's fine. Amanda tells Jim that she should go spend time with Laura in the living room.

While Amanda and Tom do the dishes, Laura gradually warms up to Jim. She reminds him that they knew each other in school, and the he used to call her "Blue Roses. Jim expresses shame that he hadn't initially recognized her. They reminisce a little, and the subject Laura's leg braces comes up. She says she feels like it makes a dreadful noise, but Jim says he never noticed it. Then the subject of Jim's engagement comes up, he tells Laura that he never had been engaged, but that his girlfriend had put that announcement in the yearbook without telling him, and that they don't see each other anymore. Laura and Jim continue to converse, and are getting along stunningly.

Laura even shows Jim her glass collection. They inspect the unicorn, and note that it must feel lonesome because it's so different than the others. They place it on a different table for a "change of scenery." The two become increasingly flirtatious, Jim boldly, and Laura, predictably shyly. When the music from the dance hall starts up, Jim asks her to dance with him. Laura is awkward and ashamed, but Jim puts her at ease. However, they jostle into the table they had put the unicorn on, and knock it over, breaking the horn off. Jim apologizes, and Laura says that it's okay she will pretend it had a surgery to make it feel less freakish.

The flirtation escalates yet more. Jim complements Laura's looks and her character. And finally, he kisses her, but it's immediately clear that he regrets doing it. He confesses that he is in love with a girl named Betty, and that he isn't in a position to court Laura. Laura is shocked and heart broken. She gives Jim the broken unicorn as a souvenir of their night together. Amanda comes in the room as he is leaving, and tells him to come again soon. He tells Amanda about his plans to marry his current girlfriend and leaves.

Amanda is furious, and accuses Tom of knowing all along and playing a cruel joke on the family. Tom is annoyed by her accusations, and again tells her that he is going to the movies. Amanda tells her son that he is incredibly selfish, and infuriated, Tom leaves.

Tom returns as the narrator and explains to the audience soon after that night he left St. Louis. As Tom speaks Amanda and Laura are visible through a transparent fourth wall, Amanda is comforting Laura. Tom talks about how time is "the longest distance between two places", and how he spent a long time searching for something he didn't know how to name. Tom explains that even though he left his family, his family never left him, and that he is haunted by their memory. Eventually, he says goodbye, but it's unclear if he's saying it to the audience, or to Laura.