Scoring System ArgumentOutOfRangeException Error

Ive been trying to do this scoring system for weeks but i still seems to get stuck and i have no idea why :( it comes up with an error of "ArgumentOutOfRangeException: Argument is out of range. Parameter name: index"

 using UnityEngine;
 using System.Collections;
 using System.Collections.Generic;
 
 public class SaveLoad
 {
     public static string name = "Enter your Name";
 
     private static List<HighscoreHolder> score = new List<HighscoreHolder>();
 
     public void Start()
     {
         List<HighscoreHolder> score = new List<HighscoreHolder>();
     }
 
     public static void Save ()
     {
         Load(); // Load current highscore list for comparison
         
         if (GameManager.score > score[4].playerScore)// If you get a high score
         {
             name = score[5].playerName; //input player name into temp highscore
 
             score[5].playerScore = GameManager.score;
             
             //Sort array by score
             score.Add(new HighscoreHolder { playerName = name, playerScore = GameManager.score });
             score.Sort((s1,s2) => s2.playerScore == s1.playerScore ? 0 : (s2.playerScore < s1.playerScore ? 1 : -1));
             while(score.Count >= 6)
                 score.RemoveAt(5);
 
             //Put Score array top 5 back into player prefs
             for (int i = 0; i < 5; i++)
             {            
                 PlayerPrefs.SetString("Name" + i, score[i].playerName);
                 PlayerPrefs.SetInt("Score" + i, score[i].playerScore);
             }
         }
     }
     
     private static void Load ()
     {
         SetDefault();
 
         for (int i = 0; i < 5; i++)
         {            
             score[i].playerName = PlayerPrefs.GetString("Name" + i);
             score[i].playerScore = PlayerPrefs.GetInt("Score" + i);
         }
     }
     public static void SetDefault()
     {
         if(SaveLoad.score[0].playerScore == null)
         {
             PlayerPrefs.SetString("Name0", "Josh");
             PlayerPrefs.SetInt("Score0", 1000);
             
             PlayerPrefs.SetString("Name1", "Peter");
             PlayerPrefs.SetInt("Score1", 500);
             
             PlayerPrefs.SetString("Name2", "Sarah");
             PlayerPrefs.SetInt("Score2", 250);
             
             PlayerPrefs.SetString("Name3", "Jamie");
             PlayerPrefs.SetInt("Score3", 100);
             
             PlayerPrefs.SetString("Name4", "Homeless Guy");
             PlayerPrefs.SetInt("Score4", 50);
         }
     }
 }
 
 using UnityEngine;
 using System.Collections;
 
 public class HighscoreHolder
 {
     public string playerName;
     public int playerScore;
 }