A : 1
A - A : 2
A - A - A : 3
A - A - A - A : 4
A - A - A - A - A : 5
A - A - A - A - E : 6
A - A - A - A - I : 7
A - A - A - A - O : 8
A - A - A - A - U : 9
A - A - A - E: 10
...
-> DFS
import java.util.*;
class Solution {
    Map<String, Integer> map = new HashMap<>();
    int count = 0;
    
    public int solution(String word) {
        dfs("");
        return map.get(word);
    }
    
    private void dfs(String word) {
        if (word.length() > 5) return;
        
        map.put(word, count++);
        
        for (int i = 0; i < 5; i++) {
            dfs(word + "AEIOU".charAt(i));
        }
    }
}