How can I get my enemy to hurt/kill player

Is there something wrong with this script:

 using System.Collections;
 using System.Collections.Generic;
 using UnityEngine;
 using UnityEngine.AI;
 
 public class EnemyAI : MonoBehaviour {
     private Animator anim;   
     private NavMeshAgent enemy; // invoking my NavMesh in the scene
     private GameObject player;
     private float AttackDistance = 3f; // distance at which my enemy will attack  the player
     private float WalkingDistance = 30f;// distance the enemy will start to run toward the player
     private int enemyHealth = 10;
     private bool isDead = false;
 
     private float timerCount = 4f;
     private float timerMax = 5f;
     public GameObject myEyes;
     
    
 
     // Use this for initialization
     void Start ()
     {
         player = GameObject.FindGameObjectWithTag("Player");// enemy will look for the Gameobject with the tag player
         enemy = GetComponent<NavMeshAgent>(); // im getting the component from start of game
         anim = GetComponent<Animator>(); // im getting the ANimator component
         
     }
     void damage(int damageAmount)
     {
         anim.SetTrigger("Got_Hit");
         enemy.speed = 0;
         enemyHealth -= damageAmount;
         timerCount = 0;
         if (enemyHealth <= 0)
         {
             anim.SetBool("Is_Dead", true);
             isDead = true;
             myEyes.SetActive(false);
         }
     }
 
     // Update is called once per frame its going to happen as i play 
     void Update ()
     {
         if (isDead)
         {
             timerCount += Time.deltaTime;
             if(timerCount >= timerMax)
             {
                 GameController.instance.enemiesOnScreen--;
                 Destroy(gameObject);
             }
             return;
         }
         timerCount += Time.deltaTime;
         if (timerCount <= timerMax)
         {
             return;
         }
 
         // enemy.destination = player.transform.position;  // assigning the NavMesh equal to the position of the Object labeled player
         enemy.SetDestination(player.transform.position); // this is the same as above 
         if (enemy.enabled) // if the NAvMeshAgent is Enabled (true or false)
         {
             float dist = Vector3.Distance(player.transform.position, this.transform.position);// getting the distance between the player and the zombie(this is Attached to)
             if(dist < AttackDistance) //if the enemy is less than the AttackDistance then the  Attack animation will play and the Run Animation will stop playing
             {
                 anim.SetBool("In_Range", true);
                 anim.SetBool("Player_Detect", false);
                 enemy.speed = 0f;
                 FacePlayer();
                 //ADD PLAYER DAMAGE SCRIPTY BITS
             }
             if (dist > AttackDistance && dist < WalkingDistance) // if the enemy is more than the AttackDIstance and less than the WalkingDistance the run animation will play and the Attack animation will stop playing
             {
                 enemy.SetDestination(player.transform.position);
                 anim.SetBool("Player_Detect", true);
                 anim.SetBool("In_Range", false);
                 enemy.speed = 1f;
                 FacePlayer();
             }
         }
         
     }
     void FacePlayer() //makes sure the enemy faces the player 
     {
         Vector3 direction = (player.transform.position - transform.position).normalized;
         Quaternion lookRotation = Quaternion.LookRotation(new Vector3(direction.x, 0, direction.z));
         transform.rotation = Quaternion.Slerp(transform.rotation, lookRotation, Time.deltaTime * 5f);
 
     }
 
 }