Darn, whittling down the five is gonna be difficult... I'll list a few and then figure out the best 5.
Aquila (90's British childrens series) - I think it's probably the 2nd episode when they figure out it can turn invisible, and the realisation of the freedom possible.
The Hitchhiker's Guide to the Galaxy (books or radio play) - The description of the planet building factory floor... trying to imagine being inside a brightly lit sphere large enough to hold planets is mind boggling.
Flight of the Navigator - The moment the ship morphs into a sleek dart.... despite the film's age I still think it is up there with the most beautiful space ships in sci-fi
Doctor Who: Blink - TBH the whole episode is brilliant, but the bit where the DVD easter egg conversation is finally joined up is cool.
Jurassic Park - Naturally it's the moment they see first the Brachiosaur.
Back to the Future - The end of the dance: Johnny Be Good.
Battlestar Galactica - The first space-faring battle scene in the recent remake (can't recall if it's in the mini-series or early in the main season)
The Matrix - Obviously gonna be a popular choice, but the lobby scene is brilliant.
Firefly - Most of the series was great, but as a specific moment: River's first handling of a gun in War stories is probably the best IMO.
Donnie Darko - The time bubbles are cool, but I think the best moment is near the end when the circular nature of the story is revealed.
Misfits - Nathan discovering his "immortality".
The Fifth Element - Loads of great scenes in this, but the first glimpse of New Yorks mid-air traffic is the best for me.
Stargate: SG1 - It's kinda corny but I love the battle over the Antarctic at the end of series 7.
Stargate Atlantis - Obviously the first episode with Atlantis rising from the ocean.
Farscape - As a singular episode, "through the looking glass" is probably my favourite sci-fi ep, (maybe rivalled by Firefly's "objects in space") in particular the first glimpse of Moya being split into dimensions.
Waterworld - Dunno if this film will class as sci-fi to everyone, but the first unveiling of the mechanical sails on the trimaran is beautiful.
And if games can be included:
Star Wars: Rogue Squadron II - The Razor battle I think showed how awesome this game is (more so to me than the initial trench run)
Portal - The first time you get control of both blue & orange portals
Half-Life 2 - The actual feeling of suppression (that I at least got) in those first few minutes after getting off the train
Metroid Prime 3 - Using the Wii remote right at the beginning to power up the ship thrusters... at the time I thought it meant I would be able to freely pilot the ship at some point (so on reflections it's kinda dissapointing, but that first time was awesome)
----
I think if I were to pick 5 it would be(in no particular order):
HGttG (image taken from the recent film, though my "moment" is more from the books)
The Matrix
5th Element
Firefly
Stargate Atlantis (even though SGA is probably my least favoured SG series, the first double episode is awesome)
