Hey, I'm currently doing the Space Shooter tutorial with Unity 5 but I keep getting this error when I attempt to run the script.

All compiler errors have to be fixed before you can enter playmode!
UnityEditor.SceneView:ShowCompileErrorNotification()

This is my script:

using UnityEngine;
using System.Collections;

public class PlayerController : MonoBehaviour
{
public float speed;

void FixedUpdate ()
{
	float moveHorizontal = Input.GetAxis ("Horizontal");
	float moveVertical = Input.GetAxis ("Vertical");
	
	Vector3 movement = new Vector3 (moveHorizontal, 0.0f, moveVertical);
	GetComponent<Rigidbody>().velocity = movement*speed;

}

}

What am I doing wrong?

If you imported the tutorial assets then the scripts that came with it are wrong. At least wrong if you are using unity5.

There is an option when importing earlier assets/packages to auto correct any API issues.
I had a similar problem and doing this sorted it.

Check Filenames match Classnames.