My iPhone 5 has LTE does it mean it has 4G?

LTE mean 4g but with LTE different carriers use different frequencies so if your carrier don't use the frequency that iphone 5 support you can only get 3g

Here is a list of supported carriers, including information on which ones support LTE. Is yours on the list? http://support.apple.com/kb/ht1937

Where, exactly did you get the phone and what carrier (in which country) are you trying to use?

If you click on the link I gave you above, you will see that Zain does NOT support LTE on the iPhone.