Just FYI and maybe you already know but if the back was original to the watch and from 1971 or 1972 there would be a date-quarter stamp inside of it up to the end of quarter/year "IV 72." However if it's from 73 (or a later replacement) then that it won't have any date-quarter stamp, as Rolex stopped doing that for whatever reason, and the serial number data will remain somewhat inconclusive. Sounds like maybe there is no date stamp, as you mention the 5513 reference # inside but not that?
Either way really nice matte 5512 with so-called Non-Serif dial & GLWTS,
T.
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