My ex-boyfriend had sex with someone else while still living with me!

It has been almost 5 months since my ex ended our relationship after 11 years together. He is still living in our house until he can save money to move out. I just found out that he had sex with his ex-girlfriend. I am really sad and upset. It's really hard to see him every day while I'm breaking inside. I told him to get out and go live with her, but he refused.. said he is not leaving. Do you think it is okay for him to do this while living with me?

What should I do?