How often does July have five Fridays Saturdays and Sundays?

According to my desktop calendar, July will have five Fridays and Saturdays (and even some Thursdays) in 2016, 2021, 2022, 2027,2032, 2033, etc...

If you look at http://www.timeanddate.com/calendar/monthly.html?year=2021&month=7&country=1 you will see that 2021, 2027, 2032 do not have 5 Sundays. The other years 2016, 2022, 2033 do have 5 Fridays, Saturdays, and Sundays.

You are little confused since your first parahraph discusses Fridays and Saturdays, in which case 2021 and 2022 do indead have 5 Fridays and 5 Saturdays in July. In paragraph two above, you begin talking about Sundays

and which years in which July will 5 each of Fridays, Saturdays and Sundays.

Every month with 31 days will have 5 instances of the first 3 days in the month. This will repeat in a 5-6-5-11 year cycle and then repeat. So it should be 2016, 2022, 2033, 2039, 2044, 2050, 2056 - don't forget to consider leap year which will cause a 1 day shift.