Had sex on cd 4 the day after my period! i was very dry (no cervical mucas!) how long will sperm survive? could i get pregnant from this encounter? i have a 27-32 day cycle?

Pregnancy has been documented from exposure on any day of a cycle, including during menses. Conception not in mid-cycle would be rare except in those with irregular cycles. Sperm can survive 4-5 days in the vaginal mucus before becoming non-functional.

Pregnancy is known to have occurred from sex on any all days of the cycle. While the risk of pregnancy is low in your case, it is not zero. If you had sex less than 72 hours ago, you may consider taking Plan B. If you do not wish to be pregnant, use contraception all the time, every time. You may consider implanted contraceptive, or IUD. Practice safe sex : https://www.hopkinsmedicine.org/healt