It's a lightly circulated SMS Jefferson. It doesn't really have any value above face at this point but if you like it keep it.
Indeed, it seems worth mentioning that there were neither proofs nor “S” mint mark coins in 1965. So a really, really nice example could have been spent from a 1965 Special Mint Set (SMS). First, here is a business strike 1965 nickel from Philadelphia. And here is an SMS of the same year from the same mint. Edit: I forgot that all mints were still producing all types of coinage. I am corrected below. Thanks!
You really don't know if that coin came from Philadelphia. No mint marks on coins in 1965 1966 and 1967 but they were still produced at all 3 mints. There's no markers to determine which mint the coins came from in those 3 years.
Oh, I think I would keep it. If it was the best 1965 I have found in circulation, even if I felt it was still a face value coin.
That would prove pretty difficult for a 65' bein that there are no 6FS nickels known. and 5fs is pretty iffy with most maybe 1 in every 100.