mmm... it is quite difficult to define a list of 5 games, like many already said... I will try to put games from different categories on the list... but no FPS... hehe
1) Championship Manager/Football Manager: I was just a little kid playing "PC Futbol" (the one about the spanish Liga) when I found out a game done by Eidos Interactive that allowed you to play with the English League.... My GOD!!! I think I haven't spent more time on any game than on these games. The amount of MP games, the competitions, the games against my brothers (we played it almost daily, trying to beat each other

) ... a huge ammount of memories playing these game.
2) Civilization Series: It is more or less like the previous case, I was just a kid when I was playing with NUCLEAR WEAPONS on Civ1!!!

(I only had 11/12 years)
I will include here the Colonization games too... I really liked trying to liberate my country from the oppresing european power.
3) WIA+AACW+ROP: I do not include here PON because I have never played it to really have fun... I was always looking for a new bug or just testing it to see if everything worked as planned...
Surprisingly, NCP is not on the list just because it didn't had a campaign... I really loved the map and some scenarios, but without a full campaign (even if it was a sandbox campaign) it really lacks "something".
4) Wing Commander: yes, I have played these games... I was young (not a kid anymore

) when a game about spaceships blown up my mind!... it was the year 1994 and Wing Commander 3 came out... you were a character in a game that played like a movie... you could even saw some real Kilrathi for the first time!!! (well, an actor disguised as a cat flying a space ship

). It was just unbelievable for me. I had replayed that game hundreds of times... including the "Privateer" spin off that came later.
5) Fallout 2-3-NV: The "RPGer" that I have inside couldn't leave some RPG game outside this list... so, here they are. So many options, so many things to do... so little time to play.
5') Mass Effect 1+2+3: Yes, I have added another 5, because I couldn't decide between them... Mass Effect was for me the first Action+RPG from BioWare that really worked, a great idea and an awesome design. Each chapter on the saga improved the previous game... not like the horrible Dragon Age 2 (I hated it soooo much), these were just amazing. I can't remember another time were I was waiting for the final chapter of a saga like I had with ME3. I even like the end of ME3 (some hated it

).
Many games were left outside of the list to try to keep it simple, like Panzer General series, Close Combat series, Gran Turismo (yes, I like driving simulators too), SWOTL, The Total War Series (I have played them all!!!), etc...