You are correct, sir, there is no mint mark. It's not supposed to have a mint mark because it was minted at Philadelphia.
Actually none of the 1965, 1966 or 1967 US coins have a mint mark. And they were produced at all 3 mints, there's no way to tell if it was produced in Philly or not. Coins before 1965 and after 1967 without a mint mark are all Phillies. It's certainly a decent looking 1965 although it has a gouge in the center. Also always show both sides, and sometimes the edges and rims. As for SMS I don't know. But probably not.
Truth be told, we will never know where the coin was minted as mint marks were not used on U.S. coins from 1965-1967: https://www.ngccoin.com/news/article/711/. This source from 2003 indicates most 1965-dated nickels were minted in Denver; it's even possible this coin may have been minted in San Francisco as the mint there resumed the minting of circulating coinage in 1965.
