After I initially add score it keeps adding.

Questions & Answers
1

Once I destroy a game object that is supposed to add 5 points to my score it continuously adds points. How do I fix this?

using UnityEngine;
using System.Collections;
using UnityEngine.UI;

public class Code : MonoBehaviour {
	public int score;
	public Text scoreText;
	
	public GameObject enemy;
	public bool enemyDead;
	// Use this for initialization
	void Start () {
		score = 0;
		
	}
	
	// Update is called once per frame
	void Update () {
		if(enemy == null)
		{
			enemyDead = true;
		}
		if(enemyDead == true)
		{
			score += 5;
			
		}
		DisplayScore();
		
	}
	public void DisplayScore()
	{
		scoreText.text = "Score: " + score;
	}
2

once the score incrementation has been done the first time we need to flag that the code has been executed before

bool enemykilledflag = true;
  if(enemyDead == true && enemykilledflag)
         {
             score += 5;
             enemykilledflag = false;
         }
3

The fix that @Tymewiz provided gets rid of one score adding loop problem. The current thing that I see causing an issue is that unless you are assigning the enemy gameobject in the inspector it will always have the default value of null.

@Tymewiz fix:

 using UnityEngine;
     using System.Collections;
     using UnityEngine.UI;
     
     public class Code : MonoBehaviour {
         public int score;
         public Text scoreText;
         
         public GameObject enemy;
         public bool enemyDead;
         
        private bool enemyKilledFlag;     
    
         // Use this for initialization
         void Start () {
             score = 0;
             
         }
         
         // Update is called once per frame
         void Update () {
             if(enemy == null)
             {
                 enemyDead = true;
                 enemyKilledFlag = true;
             }
             if(enemyDead && enemyKilledFlag)
             {
                 score += 5;
                 enemyKilledFlag = false;
                 
             }
             DisplayScore();
             
         }
         public void DisplayScore()
         {
             scoreText.text = "Score: " + score;
         }