That's a tricky question, but let's try-it
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A D20, level based, high fantasy game, so let's say D&D/Pathfinder or one of the many clones
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A prompt based, narrative immersive game with a lot of bleed potential let's say Alice is missing
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A horror games, I would say Call of Chtulhu because it's the classic one, but also to show player a percent-based skill mechanic
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Iron-sworn in GM-less mode, as it ticks both the narrative consequence driven game (PBTA) and the GM-less box
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A sci-fi game, in order to get a recent design, and a sample of dice pool I would say Coriolis
Only 5 games is actually quite restrictive, especially to show different game type and mechanics. I am a bit annoyed that I didn't found any slot for Vampire/World-of-Darkness (considering how popular is the franchise) and that Iron sworn is the only PBTA (especially considering it's not the classical PBTA) I would also love to add a Cyberpunk game (Shadowrun or Red) as it's also a popular franchise, extend the D&D clones with OSR, and add Blade in the Dark considering it's massive influence on the recent RPG scene