How to tell her?

My cousin and her husband are still married but they haven’t been together for 10 years according to both of them they are over each other well I met my cousin husband over at my friends house not knowing that it was my cousin husband because I never once met him well him and I started talking and once we started catching feelings for each other I found out who he actually was and now I am 5 weeks pregnant by her husband and I feel like I betrayed my cousin and she is going to find out sooner then later so my question is how would I tell her I am pregnant by her husband? I am the type that likes to be honest and don’t like to keep Secrets also how can I move pass this and fix my relationship with my cousin?