Me and my fiancŽe had intercourse Dec 3rd and I got my period December 5th is it possible I can be pregnant?

Probably not if you got your period. Periods stop when a women gets pregnant.

Most probably not. But it DOES happen. My grandmother and mother both continued to have a monthly period during the whole pregnancy. But that is NOT normal. And should be monitored by the doctors.
If you feel you may be pregnant, but don't feel your home tests are reliable, go see your doctor.
Good luck!

IS it a normal period? Often you could have a very light one that only lasts a day or two.

Rare to have a regular period.