I had sex with my partner 5 weeks ago and supposed to be my period will come on Monday but it does not come. For 3 week going to 4 weeks I experienced lower back pain, cramps, headaches, breast tenderness , some nausea, is there a possibility that I'm pregnant?

Possibility, yes.
If I were you, just to be on the safe side... take an at home pregnancy test.
Buy an ODD number of tests. Like 3 or 5 so you know if you are or not for sure. Pharmacy ones are the best BUT you can also find pregnancy tests at the dollarstore which work the same way.
Early morning pee is best too.
Good luck.