Coinfanmorgan ... pleased that you are sharing these coins with us as you grow and learn as a collector.
I've read and replied to several (many) of your threads ... and get the general impression from the nature of your questions that you are in the formative learning stages of acquiring knowledge.
That's great ... we all started at the same place and the CCF family is a tremendous resource of interested folks who will gladly help ... myself included. Ask away.

To this coin ...
It is indeed most likely a Proof 1962
Jefferson nickel. It will most likely have Full-Steps (FS) due to the method of proof manufacture.
It is impossible for any of us to offer an educated technical grade with the glare photos you presented with the coin inside a 2x2.
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but is there a safe way to remove it from the holder?
Take a pair of scisssors and cut the cardboard 2x2 ... or ... use a stapler remover to remove the staples ... or puncture the plastic window and slide the coin out. Stay away from the coin while doing this.
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So I'm guessing it's worth sending it to PCGS?
Hmmmm ... consider that a PF65 1962
Jefferson nickel (if yours grades at that level) has a market value on the order of $2.
Getting it into a PCGS slab will cost your on the order of $30 (grading fees plus shipping and insurance both ways). That's assuming you have already paid to have PCGS submittal privileges ... if not ... you will need to also pay a dealer to submit it for you.
Do the math and let me know how that works for you.

Not all nice coins need to be in slabs ... many folks just enjoy them as they are.
David