Helper class for using the Facebook API with Unity v5, makes use of the excellent SimpleJSON class to decode JSON objects https://gist.github.com/darktable/1411710

Demo.cs

using UnityEngine;
using System;

public class Demo : MonoBehaviour {

  void Start() {
    new FB_Query("/me", callback);
  }
  
  public void callback(SimpleJSON.JSONNode result) {
    Debug.Log("Name: "+result["full_name"]);
  }
}

FB_Query.cs

using UnityEngine;
using System;
using System.Collections.Generic;
using Facebook.Unity;
using SimpleJSON;

public class FB_Query : MonoBehaviour {

    static private List<string> perms = new List<string>() { "public_profile", "user_friends" };
    private string query;
    private Action<SimpleJSON.JSONNode> callback;

    public FB_Query(string _Query, Action<SimpleJSON.JSONNode> Callback) {
        this.query = _Query;
        this.callback = Callback;

        if (!FB.IsInitialized) {
            FB.Init(CheckLoggedIn);
        } else {
            CheckLoggedIn();
        }
    }

    private void CheckLoggedIn() {
        if (!FB.IsLoggedIn) {
            FB.LogInWithReadPermissions(perms, MakeAPICall);
        } else {
            MakeAPICall();
        }
    }

    private void MakeAPICall() {
        FB.API(this.query, HttpMethod.GET, Result);
    }

    private void MakeAPICall(ILoginResult result) {
        MakeAPICall();
    }

    private void Result(IResult result) {
        var data = JSON.Parse(result.RawResult);
        callback(data);
    }
}