4 weeks and 5 day negative test

Little

So my last menst. was 12 of June, we had a lot of sex after the cycle, tgis Monday i've done test i have morning sickness, a little bit of cramps and a huge mood swings i cried on cartoons like it was sad but it acually was funny one. Could test be negative if it was done early?

I read somewhere that HCG levels should show in 5 week of pregnancy?