Not to criticize anybody, but being indefinitely stuck on an island , with only 5 games, it wouldn't make much sense to take any story based game along.
As much as I love Mario and Luigi, Castlevania,Zelda and Ace Attorney, I don't see myself replaying those games over and over again. Maybe once, like you re-read a good book after a few years, but on a desert island, it wouldn't work.
So if I had to decide, I would take games that can't actually be completed or arcade style, with a high replay value.
Games like TETRIS, can be played over and over and never get boring ( heck I've been playing it since 1986 ).
Also somebody said MKDS, that's a good candidate, after unlocking every curses you can still play it as much as you want because it's just fun and unpredictable AI will make it different every time you play.
Space Invaders extreme also would be cool.
Konami arcade collection is just perfect, a bunch of timeless games with the highest replay value all packed in one cart !
I'm sure I didn't think it trough and I left someting really good out ( maybe Galaxy Wars ? ) but you get the message on what type of games I would take with me hypothetically .
In reality I would take my AK2i, packed with 4GB of games and homebrew, with one homebrew that would kick them all and last me for years : ZXDS ( Spectrum emulator along 5000 8-bit games from the past ) !!!