This situation occurs when August 1st is a Friday, then August 29th is also a Friday and the 30th is a Saturday and the 31st a Sunday - making 5 Fridays, 5 Saturdays and 5 Sundays in the month.
This happens this year - 2014 : the next time this occurs is 2025.
March
ummm...never.
It has 5 Fridays, 5 Saturdays and 5 Sundays.
About twice each year
every 823 years.
October 2010
Never.
March is the only month in 2013 that meets those specifications.
2021, 2027, 2032, 2038, 2049, etc.
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.
This happens in any 31-day month starting on Friday (such as July 2005).
A month always has 28 or more days, so as there are 7 days in a week there are always at least 4 Saturdays and four Sundays in a month. As most months have more than 28 days, there can be up to 5 Saturdays and up to 5 Sundays in a month.