So is it possible to have a positive pregnancy test from just after five days of one intercourse or did it have to happen prior?

If ONE intercourse.. It makes no difference (doesn't matter) when the test turns positive if there was only one intercourse. With a positive preg. Test and one intercourse, it happened... Regardless if whether it was 1 day, 5 days, or 15 days after that one intercourse, the positive test happened. If there was more than 1 intercourse, then look earlier, as a preg. Test almost always takes over 5 days to be positive.