Being limited to only one player cuts down on the utility of a lot of systems. I will also note that specifying only 5 RPG books rather than only 5 RPGs benefits games that are more compressed (i.e. it's hard to justify 3/5 of the selections for a single game). I'll assume that I also have anything needed to play the games (i.e. pencil, paper, dice).
Selections:
Dresden Files RPG - Your Story
Dresden Files RPG - Our World
Hero System 5th Edition
Fading Suns 2nd Edition
Ptolus
Honorable Mentions:
Starblazer Adventures
Earthdawn Player's Compendium
Earthdawn Gamemaster's Compendium
War of the Burning Sky Compendium
I love the Dresden Files, and it would be good to have as reading material, as I haven't read it yet, and it's also something I would love to play. Hero System is just fun to build characters for, and can be used for any genre. Ptolus is great for generating tons of ideas for medieval fantasy games. Fading Suns is one of my favorite science fiction games, and I love the world.
For the honorable mentions: Starblazer Adventures is massive and would be very useful (ony losing out as it is FATE-based as is Dresden Files). Earthdawn is a fun read and also has a ton of material in those two books, but doesn't make the cut because like D&D it's really meant for multiple players, and it would eat up two slots on the list. War of the Burning Sky loses to Ptolus as I prefer having a more open setting to having an adventure path.