Me [28 M] with my wife [27 F] 5 years together, I cheated a long time ago the other woman sent me a letter. [UPDATE]

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So I kept waiting until I was finished with work but it felt like forever and I wanted to get home already. While I was driving I kept going over everything that happened and everyone's advice about it and I calmed down and just bit the bullet.
I came home she made dinner for us, after we were watching TV and I told her I had to show her something. I showed her the letter and she looked a little hurt but I knew it would bring up bad past feelings.
She opened it and read it and than showed it to me, it was basically the other woman asking if we could get back together and that she felt something so I must have felt something as well.
My wife did stop reading because it was starting to go into detail of what we did. She asked me if I had any contact with her which I haven't and also asked if I felt anything for her which again, I don't have any feelings for the other woman.
So we talked about it more and while it was uncomfortable for me I imagine it must have been extremely hard for her. I answered all her questions and she did say she appreciated me showing it to her and us reading it together, that it felt like we were a team.
It was a very productive conversation and she said she's starting to trust a little bit again. It was still early so I ended up getting us some ice cream, in the end it worked out fine she felt good and I feel like I'm making progress its slow but worth it.
Thanks everyone for the advice.
TL;DR: I showed the letter to my wife it was just the other woman asking if we could get back together, we talked about it and she appreciated that I showed it to her.


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