Hi Wishes,
Thanks for sharing your story. I think you need to ponder on it a bit more to see if you can get it a bit clearer, and I hope that writing into the forum will help with this.
Just because you feel a 'connection' with an historical person does not mean that you
were that person. There is certainly no need to be considering bending the space-time continuum to accommodate this feeling. There are several possible simpler explanations for your feeling of affinity:
1. You just 'identify' with them for whatever present life reasons because you see certain similarities as you have described.
2. You may have known this person in your previous incarnation - for example you could have been an older relative or a sister - therefore you feel an affinity/familiarity with them, even to the extent of physical resemblance.
3. You and this person may have spent more than one life together.
4. All of the above.
However, all that said, do you have any idea of the circumstances of the person's death? Since you were born four or five years or so before they died, do you have any idea if that person spent the last five years in a coma or similar? In that way it could be possible. There is a belief that sometimes the soul has already left the body in such a situation, although with modern techniques the body can live on for some time - just without any awareness or consciousness.
My suggestion would be to do some reading and deep thinking on the whole topic of reincarnation and take a look at the FAQs. There are some very good points in there. Many people have stumbled along this road ahead of you! You may want to try some of the techniques for regression out for yourself and see if you can uncover any actual memories of your most recent incarnation and see if they make any sense with your feeling.
In this way you will not only begin to explore your own personal mysteries, but maybe clarify the relationship with this person from the past who fascinates you so.