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 get 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