The case number between the lugs at 6 does not match the case number engraved inside the case back of this watch. It would appear that the original case back was accidentally changed during servicing by the Ministry of Defence.
The reference 5513 became the first Rolex for many years to become an official British Military issue watch, when it was issued to the divers of the Royal Navy in 1965. The military requested certain modifications; in this case the modifications were so major as to almost be a new watch. First, they wanted a new dial featuring a large "T" in a circle under the center post. The high visibility hands were much larger and of a completely different shape. The hour hand was diamond-shaped, while the minute hand was much wider than on a conventional Submariner and the seconds had had a unique luminous diamond indicator at the tip. Even the case was different from a standard Submariner. On the military models the spring bars were replaced with solid steel bars welded into the spring bar holes. The case was then polished so the hole was hardly visible. The rear of the case was then engraved with all the military specifications and issue numbers which enabled the quartermaster to identify the watch.