Heres a method that was passed on to me and would cover your fertile dates. Starting on day 6 of your cycle have sex whether you are bleeding or not. If your period started on 5/7 than 5/13 would be the day to start this. Have sex every other day through day 15. If you have a long cycles then you can extend it to day 20. Everyone who did this got pregnant within 2 months. It keeps live sperm in your system around the clock. I used this method myself twice and 5 of my friends have used it.
To answer your question based on your cycle dates your fertile days would be May 20-24 with your most fertile days being 22-23. The 23rd should be your actual day of ovulation.
That method sounds promising, also make an account on mymonthlycycles.com to track your period and also your fertility. If you fill in your account history, recording the dates you got your period, it calculates your fertility based on your history and your personal cycle, so its pretty accurate. It shows you ALL your fertile days for up to three months in advance. If you make an account and get stuck on setting up just ask me =)
I agree with Sharlene, I think you ovulate between the 22nd and the 23rd. If you want to get pregnant, start having sex three days before you are due to ovulate, all the way until four days after you ovulate.
The old wive's tale is that if you have sex the three days before ovulation you'll get pregnant with a girl, and for the three to four days after you ovulate you'll have a boy; the theory being that girl sperm lives longer and boy sperm swims faster. Who knows if its true... but I tried for a girl and I have a girl.
Just keep in mind people can ovulate at different times. We don't all ovulate mid month, although this is most common. I had a friend who was desperately trying to get preg. and she found out she was ovulating the day after her period. She got a thing from the chemist that with a drop of your saliva can tell you when you are ovulating. Also many women have a gel like discharge when they are ovulating so watch for signs of this.