It is better if Alice stores her password on a 3x3, as we can
Guess of the centers, as they are fixed, and find out the other pieces, by tracing the 7 turns, and just having one face as the input after that.
In the case of a 5x5, it gets tricky, as
The number of possible slice moves increases, and also the the centers of two kinds (x centers at the corner fringe, and + centers at the edge fringe), cannot be deduced, even if you are given the information of 5 sides, and one side is hidden.
The reason being
That there are nifty amount of 2-cycles that can be put up on this centers, making them untraceable unless we have the visual of all the 6 sides.
On the other hand
A 3x3 , has 4x10^17 possibilies, letting us store even a 10 digit ASCII code password quite easily, if we form a map between each state, and a string of ASCII characters (this will be a tedious task), but a 3x3, or multiple 3x3, solves the problem.
If your password is quite long,
Then there is one more fantastic solution, you can have 2 cube states added onto a single 3x3 cube : eg, U D M B' U' S R' S' R U B M' U' D' + F E F2 R' S' R S R' E' R F, and you can retrieve it by some computational factoring algorithm, the same way we try to factorise big prime numbers during encryption.
See this video for more clarity on what I mean by adding cube states:
Adding cube states