Also there is a "gimme" list that are episodes that are generally so universally acclaimed that everyone is likely to want them.
Given the prospect of long-term isolation, I don't know if I'd want to be reminded that death may serve a greater purpose (City on the Edge) or that some absences are too difficult to get over (The Visitor), whatever the respective merits of the episode may be. On the other hand, I probably wouldn't choose, as the things I had with me, five hours of television. I would prefer several long, complex works of literature (like Musil's The Man Without Qualities or Jabès' Book of Questions), a telescope and a music instrument.
However, if it must be five Trek episodes, I wouldn't pick my most favorite, but those that would occupy me best in that situation:
The Omega Glory
Chains of Command 1 & 2
The Way of the Warrior
The Forge (I'll have to use my imagination on the continuing episodes)