Are there several versions of the book? In my copy 5.5 says "un point x de X est une générisation d'un point y (et y est une spécialisation de x) se y est adhérent à {x} dans |X|" and this means exactly that y is contained in the closure of {x}, see http://fr.wikipedia.org/wiki/Adh%C3%A9rence_%28math%C3%A9matiques%29 Also x and y are arbitrary points here, not necessarily closed.

Are there several versions of the book? In my copy 5.5 says "un point x de X est une générisation d'un point y (et y est une spécialisation de x) si y est adhérent à {x} dans |X|" and this means exactly that y is contained in the closure of {x}, see http://fr.wikipedia.org/wiki/Adh%C3%A9rence_%28math%C3%A9matiques%29 Also x and y are arbitrary points here, not necessarily closed.