OP I have been in a similar situation to you, although he told me he cheated with prostitutes because I had been sexually abused as a child (the logic being that abuse as a child left me dirty or broken or some other bollocks, who knows) he was the first person I confided that to, and he used it to excuse hurting me, so I get a little of how you are feeling right now.
It is just over two years later from when I found out and I will tell you a little bit of what I now know, it felt impossible to leave at first, I felt humiliated, ashamed and disgust at my own appearance, references to anything sexual left me feeling ill, I went through almost a full year of not being able to watch films or television, no new music, no new books for fear there would be references to sex, escorts, cheating or any type of infidelity. I was very cut off and alone from friends and family, I cried everyday, I still cry most days, I just felt overwhelmingly sad and anxious.
I tried counselling with next to no success at first, I then found an excellent therapist who specialized in infidelity due to the use of porn and sex workers, she had heard it all before and just allowed me the space to cry it all out without shame or embarrassment, eventually I was diagnosed with PTSD because of what I found during the initial discovery of what he had done.
Everyday is a struggle still but that struggle grows less all the time, I cannot reconcile the man I knew and loved with the person who used sex workers, he is a stranger to me. In the early days I stayed and tried to "understand" and make things right between us, it made no difference, he didn't try at all, I was just expected to get past it and never ask any questions and try to talk about it. The truth is he did what he did because he wanted to and he could. No big, dark emotional secret, just a selfish man doing what he wanted with no thought for who that hurt.
I knew it was over the day i bought a specific household item for "my" new home that I had started to build in my own imagination, I knew I was done when I could not see him in that home with me, and that thought no longer frightened me. You will get there in your own way and your own time.
To those telling the OP to get some self respect, please stop. Words like that hurt us further, we do not lack self respect or backbone, or anything else you may think of us, we are people who have been abused by those who said they loved us most. People who cheat repeatedly are abusers, they financially abuse us (using household income to buy access to other women's bodies) they emotionally abuse us (lying and blaming us when caught, threatening us with our most intimate vulnerabilities that we told them as we trusted them ) they physically abuse us (having sex with strangers and exposing us to STI that can be life ending) they are every bit the abuser that the person who punches their spouse is, the abuse is just hidden and not seen by others.
OP take care of yourself, think about what you really want and need in life, it is never to late to make a change, please reach out to family and friends to support you, if you can please check out the book "Intimate Deception: Healing the Wounds of Sexual Betrayal " by Sheri Keffer, I found it very helpful, please be kind to yourself.