Slightly freaking out!

*No judgments please! I take full responsibility for what happened and what could happen, I just looking for an answer*

I’m 5 weeks pp and I don’t get my birth control until 1/26. Well one thing lead to another and me and my husband ended up having sex on 1/16. He did pull out(I know that’s not always effective). Would a test show up positive by 1/26? I wasn’t tracking when I got pregnant with my daughter so I’m sure how the whole dpo thing works. I feel REALLY dumb for asking this but I need an answer.