There's a chance you could be pregnant. Any symptoms? I recommend taking a test just to be sure though you may have to wait a week or so. Don't freak out yet! Goodluck
The pull out method is not a form of birth control. You can still get pregnant from doing this because there's pre semen.
You really can't go by a period tracker because not all women ovulate in the middle of their cycles. The only way a woman can know for sure when she ovulates is to use an ovulation kit for several months.
You're right, sperm can live up to 5 days in a woman's body
Can I ask why you didn't use some form of protection? Condoms can be bought almost anywhere, even at gas stations. I understand these things can happen in the heat of the moment so that's why you should always carry condoms with you.
All you can do right now is wait a couple more weeks and take a pregnancy test. If it comes back negative I highly recommend you go to a women's clinic to get birth control. They will give you condoms for free any time you need them and they will also offer the pill, the implant and several other forms of birth control at little to no cost depending on your income. Research women's clinics in your town.