She is not definitely your 3rd to 5th cousin, as Gadget says. This is purely an estimate, but even if it were correct, that could still indicate that you share 2G to 4G grandparents, or even more distant.
If you have a well documented tree going back as far as your 4G grandparents, all 64 of them, (possibly as far back as 5G, 128) you will have done a lot better than most people (taking into account missing fathers, missing mother's names, lack of records etc).
If she has done the same as well you have a chance of finding the link between yourselves, assuming that there is a link.
Seeing as neither of you appear to have a public tree to compare, your chances are very much reduced.
You say she has one suggestion, her great grandmother from Kettering, presumably (?) the only known ancestor of hers from UK. If she has someone else from UK that she doesn't know about for reasons given in 2nd paragraph above, you could be looking at the wrong person completely.
But if it is the link, her great grandmother has several ancestors as well, you could have to go back potentially 3 to 4 generations before you find a connection.
Apart from using shared matches, personally I wouldn't follow this up, until anything further comes up. It's always nice to be contacted though, I seem to do most of the contacting.
Regards Margaret