Wow, congrats on the 5513! Great investment!
The crown is the original 1st incarnate of crowns used on 5512 and 5513. Rolex used caches of parts as they saw fit, thus certain discrepancies are bound to arise. For example, my 1675 is from '67 but it has a small GMT hand. How is this possible? Well, for one, I am the 2nd owner. The first owner was my grandpa. He bought it from Rolex Tokyo new in box. The watch was never serviced until I got it. And Rolex BH verified that mine came with the small GMT hand (rare on this late of a 1675, but true). The small hand used on mine is a perfect example of ROlex using up freshly discovered caches of parts. The same can be said about certain dial repalcements during service.
Anyhow, the issue of my 5513 crown is somewhat of a mystery. There are plenty of collectors on TZ who have the same crown on their 5512/3's. I am not alone. I would like to solve this mystery though (at least, I'd like to get the parts numbers for both the crown and the tube). I just wish that I was not dumb enough to have thrown out the parts number for the NOS crown when I bought it. ARRRRGH!!!
There were many variations of crown markings as you know. This adds somewhat to the confusion. My 1675 Twinlock crown has a line under it.