Which Month Was Quintilis?

Roman counting is confusing since it is inclusive, so if, for instance, you want to know how many days there are in a week, using the Roman system, you would have to include both Sundays, as well as the days in between. The answer would be octo '8' (as in October). The calendar is confusing for many reasons. For those who understand the Latin for the numbers, it is puzzling to see that, for instance, September is not the seventh month of the year, since the Latin for 7 (septem) is clearly present in the word. There is no inclusive counting involved in determining which month is called the fifth. The Roman word for 'five' is quinque and the Latin for 'fifth' is quintus. Do you know which month is Quintilis or Quinctilis?

If not, see Which Month Was the Roman Quintilis?