Does a late positive pregnancy test mean due date could be off?

Madison

I got my first response positive only after 5 days after my missed period. When I went to the dr. Expecting to be 6 weeks based off of my LMP they only measured 5 weeks. I go back on feb. 8th but I’m freaking that something will be wrong and the pregnancy will not continue. But since I didn’t get a positive until I was 5 days late I’m hoping that makes sense as to why I was a week behind. Freaking out. Anyone ever experience this?