Using MS Works calendar - the last time it happened was in 2004. The next time will be in 2021 !
About twice each year
As of 2011, the last time the month of July contained five Saturdays, Sundays, and Mondays was in 2006. The next time it will happen is in 2017.
This will occur in any month that has 31 days when the 1st falls on a Friday. In any given year, on average, one month having 31 days will start on a Friday since there is a 1:7 "chance" of a month starting on any given day of the week, and there are seven months that have 31 days in them. Simply check out the calendars for 2 or 3 years and you will find that this is a fairly common occurance.
They all have four Saturdays. However, usually only four months per year have five Saturdays while usually eight months per year have only four Saturdays.
If payday is Friday, there were five months with five Fridays in 2010.
Exactly 14% of all Decembers have five of each of Fridays, Saturdays and Sundays.
About twice each year
There is an internet hoax going around claiming that certain occurrences of five days in a month occur every 823 years. For examples, in October 2010, there were five Fridays, Saturdays, and Sundays. However, this occurrence occurs at the most every 11 years. The next time five Fridays, Saturdays, and Sundays occurs in a month is March 2013. The next time it occurs in October is October 2021.
There are 14 calendar variations (7 days of the week plus leap years). Some years October will have 5 Fridays, 5 Saturdays, and 5 Sundays. October 1999, 2010, 2021, and 2032 all have 5 Fridays, 5 Saturdays, and 5 Sundays. This looks like an 11 year gap, but October 1988 and 2043 do not have 5 weekends.
Prior to this year, July had five Fridays and five Saturdays in 2010.
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.
March, 1997 included five each of Saturdays, Sundays and Mondays and four each of Tuesdays, Wednesdays, Thursdays and Fridays.
Five Sundays: March, June, September & December Five Mondays: April, July, September & December Five Tuesdays: January, April, July, October & December Five Wednesdays: January, May, July & October Five Thursdays: January, May, August & October Five Fridays: March, May, August & November Five Saturdays: March, June, August & November
October had 5 Fridays and Saturdays and Sundays in the year 2010 and will have it again in 2021 than 2027, 2032, 2038 , all the months with 31 days in them have the same pattern 11 years than 6 years than 5 years than 6years than 11 than 6 than 5 than 6 doesn't matter where you start at 5 or 6 or 11 just do 4 in a row and it will add up to 28 years October has 5 Fridays, Saturdays and Sundays. 5 times starting in 2010 , 2021, 2027,2032 and 2038 December will have them in 2017,2023,2028,2034 and 2045 January is 2010, 2016,2021,2027 and 2038 march is 2013,2019,2024,2030,2041 may is 2015,2020,2026,2037 and 2043 and the last month with 31 days in it, July has them on 2011,2016,2022,2033,and2039
In 2008, January had four Saturdays. February had four Saturdays. March had five Saturdays. April had four Saturdays. May had five Saturdays. June had four Saturdays. July had four Saturdays. August had five Saturdays. September had four Saturdays. October had four Saturdays. November had five Saturdays. December had four Saturdays.
January, April, July, October and December in 2028 will have five Sundays.
January, April, July, October and December of 2017 have five Sundays each.