First let me say... That is a great picture and for $5 you can't go wrong.
Now.. I can't be sure from a picture on a screen, but from what I see I don't think the signature is ink. From what I see it looks like it's printed.
There are a few reaons that I say this.
The lines look to be a consistant thickness and are solid.
There are no fade spots that there would be if done with a felt pen.
There is no pooling or expanded width on stroke changes as if done with a quill.
It's not faded at all. It looks black. It would look greay(ish) if it was over 100 year old ink.
Here is a comparison of a real signature and yours.
Yours is the top one. They are both inverted and sharpened to show the lines better.
Not meant to be a downer just giving my observations.
I've been told and know by my own experience that a signature from that time period wouldn't be black or gray but a rusty brown due to the level of iron they used back then to make ink. Pen ink from that period tends to fade away and appear opaque and light rusty brown and that signature is to dark and black. I have seen many old documents and have a few myself like my great grandfathers discharge from the Navy and his and his wife's pention. That being said it's a great find and has value but I believe also it's a print. And there might be other presidents because this might have belonged to a set of presidential prints, all signed, all framed to hang on a hallway wall in a politicians office or a city hall. But please keep us all posted and it's a great $5 find. And I think the signature comparison is great but I know myself that things I sign never are completely the same so I tend to disagree with some handwriting experts opinions. However, the picture is super and I still believe it's a print and is a collectable and worth more than you paid for it, GREAT FIND !! IMHO, Woodstock