Look carefully, if that side were 5 then the side AB should be 4, not \(\sqrt{5}\). How you should solve this:
Divide ABCD in half diagonally. We have two triangles now. We apply the pythagorean theorem to triangle ABC. Then AC is \(\sqrt{30}\). Now we know that for triangle ACD, that AC is \(\sqrt{30}\) and DC is 4. Apply the pythagoren theorem again to find that AD is \(\sqrt{14}\).