Compiling a list of the greatest episodes of The Simpsons is like trying to eat your way out of a gigantic doughnut: lots of fun but completely impossible.

In spite of this, and in celebration of the show’s 500th instalment this weekend, CultBox have given it a try and chosen five of the very best…

5. Homer’s Barbershop Quartet

‘We need a name that’s witty at first but seems less funny every time you hear it.’

Homer tells the story of his barbershop quartet, the Be Sharps, who became the most popular group in the world … for five-and-a-half weeks.

Featuring Apu, Principal Skinner and Barney (who replaced Chief Wiggum from the original line-up after their manager decided a cop in the band was ‘too Village People’) the foursome achieved worldwide fame but eventually split after Barney began dating a Japanese conceptual artist named Kako. It’s a story that sounds vaguely familiar – as guest star George Harrison remarks, ‘It’s been done’ – but even non-Beatles fans can enjoy this episode again and again.

‘That’s my son up there!’ Grampa Simpson announces proudly when the group play at his retirement home. ‘What – the bald fat ass?’ a friend asks. ‘Er, no … the Hindu guy,’ Grampa replies.

4. Bart After Dark

‘Ah, the old greet ‘n’ toss. No problemo.’

Bart gets a job working the door at Maison Derriere, a house of ill-fame.

When Marge returns from scrubbing oil off rocks at Baby Seal Beach, she’s horrified to find her son employed at a bordello and joins a campaign to have the place closed down – and it’s the response to her slideshow of shame, outing what Mayor Quimby describes as ‘a small clientele of loyal perverts’, which always gets the biggest laughs.

‘My parents insisted I give it a try, sir,’ Smithers protests when Mr Burns spots him amongst the clients. ‘Oh, er … Barney!’ Moe says in tones of unconvincing disapproval when nobody reacts to a photo of his most regular customer appears.

Best of all is the scandalised double-disapproval of Superintendent Chalmers and Agnes Skinner – ‘Skinner!’ ‘Seymour!’ – and the hapless principal’s wail in response: ‘Mother!’

3. The Springfield Files

‘A lifetime of working in a nuclear plant has given me a healthy green glow … and left me as impotent as a Nevada boxing commissioner.’

Homer sees an alien on the way home from Moe’s but nobody believes his story of a close encounter; not even when Agents Mulder and Scully from the FBI arrive in Springfield to investigate.

David Duchovny and Gillian Anderson give excellent performances (‘His jiggling is almost hypnotic,’ Mulder remarks as he watches Homer on a treadmill) but they are bettered in the guest star stakes by Leonard Nimoy, who introduces the show.

‘The following tale of alien encounters is true,’ he says, ‘and by true, I mean false. It’s all lies, but they’re entertaining lies; and in the end, isn’t that the real truth? The answer is no.’

2. Who Shot Mr Burns? (Part 2)

‘Kids, as far as Daddy’s concerned, you’re both potential murderers.’

Having successfully blocked the sun from Springfield and subsequently been shot, Mr Burns lies in a coma (Kent Brockman: ‘Burns was rushed to a nearby hospital where he was pronounced dead; then he was transferred to a better hospital where doctors upgraded his condition to “alive”’) while the town tries to establish who committed the crime.

It’s a superb story with a denouement that doesn’t disappoint, but it’s for a standout scene amongst many moments of comedy genius – including Chief Wiggum’s Twin Peaks-style dream and Willie doing the Basic Instinct leg-cross whilst being interrogated – that this episode has made the cut: Moe’s humiliating lie-detector test.

‘I got a hot date tonight. (beep) A date. (beep) Dinner with friends. (beep) Dinner alone. (beep) Watching TV alone. (beep) All right, I’m going to sit at home and ogle the ladies in the Victoria’s Secret catalogue. (beep) Sears catalogue. (ding) Now would you unhook this thing? I don’t deserve this kind of shabby treatment.’ (beep)

1. Homer Badman

‘The courts might not work anymore, but as long as everyone is videotaping everyone else, justice will be done.’

Homer is falsely accused of sexual harassment after snatching a gummy Venus de Milo from the backside of a babysitter.

Literally everything is wonderful about this episode, from the Cleetus-esque farmer duped into admitting he runs a sex farm for hookers to Homer’s escape into a flight of musical fantasy about living beneath the sea (‘There’ll be no accusations / Just friendly crustaceans’), his badly-reedited interview on ‘Rock Bottom’ and the sleazy TV movie about his alleged crimes, Homer S: Portrait of an Ass Grabber.

Best of all, however, is perhaps the most mind-bogglingly brilliant Simpsons vignette of all time: Gentle Ben’s appearance as a chatshow host. The giant bear starts off sympathetic to his guests but soon loses interest when he spots a table laden with food. ‘No, Ben! No!’ protests a panicking aide but he is tossed aside, forcing the ‘Ben Control’ team to sedate the enraged grizzly with tranquiliser darts.

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