Randomizing an array and storing value to external file? [duplicate]

I am randomizing an array of strings and writing it to an external file in the system. I am also reading the contents of text file before I write to it so that the no duplicates are found. If there is a duplicate, I am recalling the function to generate a random string. The problem lies here: (a) Once the stack is filled, I get an error message saying StackOverflowException: The requested operation caused a stack overflow. (b) Once the stack is filled, the shuffle function completes the function to generate random string very slow

Is there a better way to achieve what I am doing? Right now it is only 5 array of strings. It could be a thousand later. Should I use List instead of Array?

using System.Collections;
using System.Collections.Generic;
using UnityEngine;
using System.IO;

public class GenerateRandomNumber : MonoBehaviour
{
    private string[] animals = new string[5] {"Pig", "Dog", "Camel", "Giraffe", "Elephant"};
    public string GetAnimal;
    public string word;
    string path;
    void Start()
    {
       path = "Assets/StreamingAssets/ID.txt";
    }

    void Update()
    {
        if(Input.GetKeyDown(KeyCode.R))
        {
            ShuffleAnimals();
        }
    }

        public void ShuffleAnimals()
      {
           GetAnimal = animals[Random.Range(0, animals.Length)];

           word = File.ReadAllText(path);

           if(word.Contains(GetAnimal))
           {
               ShuffleAnimals();
           }

           else

           File.AppendAllText(path, GetAnimal + System.Environment.NewLine);
      }
}