When After Intercourse Can A Pregnancy Test Be Taken?

Hi just wondering could I have conceived, the first day of my last period was the 23rd April, 2015, my cycle is usually 32 days in duration. I have been keeping record of my cycles for the last number of months as I get a pain around the middle of my cycle which I am putting down to ovulation. This pain started on the 5th May during this cycle and lasted until 9th May getting less severe. I also am keeping track of my cervical mucus and this was thicker on the 5th of May and like that clearly as the week went on and lasted until the 10th May, where is became a clear, strechy consistency. I had sexual intercourse on the 10th May where the condom slipped off and my partner ejaculated, we did not realise this had happened until we had finished. I can t take the pill as a previous clot, so I assumed I could not take the morning after pill, When is the earliest a home pregnancy test would show I was pregnant or not?