Just remember that you are not adding to a particular list-you are just giving your own list of five and some of them might be movies others have chosen…or not.
The Great Escape
Blazing Saddles
In that case, Casablanca goes to the top of the list. Number five would probably be a toss-up between the last two.
I want to say Five Easy Pieces, for one.
I have to admit that I thought of that film because of the name of this thread. But I consider it about as perfect as a film can be.
The Great Escape
Double Indemnity
The Godfather
Pulp Fiction
I want my fifth choice to be a comedy and I can’t narrow it down between Blazing Saddles, The Producers and Life of Brian.
Miller’s Crossing
Oh, and if someone says something that absolutely forces you to change your mind, just give us a new Perfect Five Movie list and we will condemn the former list to The Bowels Of Hell ™.
Casablanca
20,000 Leagues Under The Sea
Jaws
Raiders Of The Lost Ark
North By Northwest
Night On Earth - Jim Jarmusch
The Apartment - Billy Wilder
Der Himmel Über Berlin (Wings Of Desire) - Wim Wenders
Seven Samurai - Akira Kurosawa
2001 - A Space Odyssey - Stanley Kubrick
I post this with only having read the OP but not the whole thread.
Bad Santa
Anger Management
Hangover
Give me time to figure out the other two.
Miller’s Crossing
The Godfather
The Big Lebowski
A Night at the Opera
Raging Bull
In no particular order:
Network
Parasite
No Country for Old Men
Grave of the Fireflies
Harakiri
Star Wars (the original 1977 version)
Airplane!
Robocop
The Wizard of Oz
Commando
Casablanca
American Graffiti
Star Wars (the first one)
The Magnificent Seven (the first one)
Animal House
My fourth entry:
Monty Python and the Holy Grail
How could this not be perfect a movie when so many classic lines from it have been repeated for decades! 
“Perfect” being too big a word for me, I would say the following - listed chronologically – are four of the five greatest movies that I have ever seen (though only one of them is a personal favorite):
M (1931)
King Kong (1933)
Citizen Kane (1941)
Seven Samurai (1954)
The Last Picture Show
The Godfather (Part I)
Young Frankenstein
To Kill a Mockingbird
Star Wars (1, or 4, however you count it)
A Room With a View
Breaker Morant
Almost Famous
Bottle Shock
Wallace & Gromit - Curse of the Were Rabbit
I’m not sure there’s 5 perfect movies I’d agree on, at any one time, because the best movie is the one that suits your mood.
So, I’ll go with a related list - 5 movies I’d want to have with me if I was stuck in Space / 6 month trip with no internet / alone in a strange place for work / etc (and for the record, yes, I do have digital copies of all of them on my laptop and tablet, why do you ask?)
Princess Bride
Army of Darkness
Conan the Barbarian (1982 duh)
Kung Fu Hustle
Spaceballs
Note, this particular list is movies that are perfect for me, in that I can stop and watch any one of them, at any time, in nearly any mood and feel good, rather than on their direct merits. They are the perfect “comfort food” of movies.
YMMV of course.
The Seven Samurai
The Great Escape
The Apartment
The Big Lebowski
The Little Foxes