Witching hour 🥲

My 5 week old sleeps good throughout the day and night until exactly 11:43pm. Every night on the dot she wakes up. She gives hunger cues so I feed her. She nurses for 30 minutes or so then she’s wide awake. Like eyelids taped open. She will not close them for anything. Then by about 12:40am she cry’s. Nonstop. She screams and grabs for my boobs and starts rooting so I try feeding her again but she just screams and grunts while nursing and repeatedly unlatches just to scream at me and frantically root again. This goes on till 3-4 in the morning. I don’t know what to do or how to calm her. I feel bad because my SO works early in the morning so he goes to work on 3 hours because she just will not calm down. I’ve noticed the only thing that helps at all is letting her cry for a few minutes. I hate letting her cry because she just wants me to comfort her but it’s the only way to get her to sleep. If I didn’t let her cry we would be up all night. :/ I need help I don’t know what to do anymore We are all so tired.