Sleeping when baby sleeps

I literally can’t. I’m so exhausted that I’m terrified I won’t wake up from his cries. He’s a week old, and I’ve been getting about 5 hours of sleep everyday. I only sleep when his dad is fully awake, but he works & needs to sleep for work. I don’t know how to get over this fear. I don’t know what will help. I cry everytime thinking about not hearing his cries. I feel like such a bad mom because I’m so tired. I don’t know what to do. I just needed to vent.