I've got a fairly solid top 10 or so in my head but narrowing it down to 5 was very difficult. Not necessarily in order, here they are:
GTA: San Andreas (2004, PlayStation 2)
It was a toss up between San Andreas and the original Grand Theft Auto. San Andreas gets the nod because it is in my opinion the pinnacle of the series to date.
SWAT 3: Close Quarters Battle (1999, PC)
Pretty much the perfect tactical shooter. The police theme and realism (for a video game at least) put it firmly above the chasing pack.
The Elder Scrolls IV: Oblivion (2006, Xbox 360)
This game opened my eyes to the fantasy genre that I'd previously incorrectly assumed I wouldn't like.
Deus Ex (1999, PC)
An absolute masterpiece of a game. If my top 5 were in order this would be no lower than 2nd.
Mass Effect (2007, Xbox 360)
It's undoubtedly been bettered in many ways by the sequels but there's a sci-fi charm to Mass Effect that no other game has come close to. No Man's Sky almost had it but fell short.
Honourable Mentions
Broken Sword (1996, PC)
Head Over Heels (1988, Amstrad CPC 464)
Portal (2007, Xbox 360)
Rainbow Six 3: Raven Shield (2006, Xbox 360)
The Settlers III (1998, PC)
Theme Hospital (1997, PC)