As I said, many gaming franchises aren't in the poll, but it's impossible to think about all of them. I still think 5 votes aren't enough, because I'll have the feeling I'm probably missing some of my favourite ones, but let's see...
Two of my votes are very clear: RDR and GTA. Red Dead Redemption 1 is my favourite game, and probably RDR1 and RDR2 together make one of the best well-written stories. Most of the people prefer RDR2 (and they have reasons to say so, of course), but RDR1 has that
something which makes it so special. I don't know what it is, because it's worse than RDR2 in every single aspect, but this game has
something that RDR2 doesn't have, and I still don't understand it. GTA is also another franchise that was extremely entertaining for me. That trilogy from the 2000s was simply remarkable, and with mods in PC is even better. My favourite one is GTA 4. It's probably the weirdest of them, with those grey/dark colours representing a sad New York city, and it's probably the deepest of them all. Also, one of the things I really like about this game is how technical it is, with the Euphoria physics and how much you can interact with the environment. This may be a very unpopular opinion, but I think game developers should focus more on how can you interact with everything than on graphics.
I have to include Resident Evil in this "top 5" too. RE5 and RE6 were a bit weird as they tried to copy RE4's formula, but I think these games are great. My favourite ones are RE4 and Resident Evil: Code Veronica. Yeah, I know, they are very different, but they don't necessarily have to follow the same formula
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I would have voted for Uncharted or Need For Speed, but as these options would be kinda obvious I've decided to vote for Ratchet & Clank. I don't think it's necessary to describe this gaming franchise, I'll simply say I could still play all of the PS3 games if I were blind
My final vote goes for Max Payne. Matrix is one of my favourite movies, and what was the most surprising formula used in these movies? Exactly,
bullet time. Max Payne 1 and 2 represent quite well this formula, in consonance with the dramatic story of Max Payne looking for answers. Max Payne 3 doesn't have this kind of dramatic story, but it's probably one of the best third-person shooter games ever made. The bullet time was considerably improved and in this game you're going to experience the most satisfying shootings.
I'll rope in Skyrim/TES under it too tbh, because they're both similar games made by the same game studio. Fallout is easily my top favorite! I'm a sucker for heavily story-driven games. I was introduced to Fallout 3 in 2013, because I played a lot of Skyrim already at the time and somebody's comment of, "Fallout 3 is like Skyrim but with guns" is what made me start playing the series. Fallout: New Vegas was a lot of fun too (major props to Obsidian: I played their other game Outer Worlds too, and I really enjoyed it), but I'll never forget the all-nighter I pulled just to nab for myself a copy of Fallout 4 the day of its release, because I'd heard a next-gen Fallout was coming out. I just love the story and the lore its world has to offer, I know they're not for everybody but that sort of post-apocalyptic world, in its state due to an intriguing political turn of events, is so fascinating to me. BethSoft is very good at making their universes feel like living, breathing worlds and that sort of creativity has always inspired me.
I voted for Minecraft as well, I've played that on and off during childhood, and I still play it to this day, although on a personal big modpack of mine (yes, it's 1.12, yes, I know it's old. 
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