I had the same question and still don't get the answer.

My solution was (dynamic programming approach):

private static String winner(int n) {
    String[] memory = new String[101];
    Arrays.fill(memory, "");
    return winner(n, memory);
}

private static String winner(int n, String[] memory){

    if(n == 1){
        return "Second";
    }

    if(2 <= n  && n <= 5){
        return "First";
    }

    if(memory[n] == ""){
        if(winner(n - 5, memory) == "First"
                && winner(n - 3, memory) == "First"
                && winner(n - 2, memory) == "First"){
            memory[n] = "Second";
        }
        else{
            memory[n] = "First";
        }
    }

    return memory[n];

}

which is longer than this solution and recursive but makes sense to myself. I'd like to understand the reasoning of the other solution, more specifically this sentence:

mod 7 is taken because max is 5 and min is 2, so at the climax of game atmost 7 cards are left.