Can i get pregnant the day after ovulation?

So me and my husband are trying to concieve our first child. i had sex on the 17th of may. i bought ovulation strips and began taking them the 19th. on the 19th i got a positive opk. i took one on the 20th and got another positive, i took one later on that night and i got a fainter test line but still somewhat dark but not darker then the reference line. this means i ovulated right? i had sex on the 21st. so im wondering if it is possible i have gotton pregnant? i dont wanna get my hopes up only to have them crashing down again. so i guess my questions are can i get pregnant the day after ovulation? does that fainter line that night mean i ovulated or is it possible i didnt ovulate till the 21st? and can the sperm from the 17th lasted long enough to reach my ovulation?