It depends on the context. In everyday conversation usually: - "My birthday is the fifth of November." (I wouldn't use a preposition.) When giving my birthday officially, e.g. on the phone to a company: - 'the fifth of November' - 'November fifth' - 'the fifth of the eleventh' - 'five eleven' (In these cases, you're usually giving your birth date so you'd say the year at the end.) I speak British English.

With specific dates, you always use "on" in both British and American English. America writes dates as month, date, year, so in American English you would say my birthday is on August 10. In British English, dates are written date, month, year, so in British English you would say my birthday is on the tenth of August. We don't say on the ten of August.

As Tom says, you need to watch your prepositions: "in" for months, "on" for days. In the USA, we usually say, "on August tenth (also spelled "10th"). "The tenth of August" is a less common option. It may be different in Canada, and it is definitely different in the UK.

No one ever says "My birthday is in August 10" but they would say "My birthday is in August". If the choice is between (as you probably intended) "My birthday is August 10" and "My birthday is the tenth of August" I would say the second is more common in conversation, but the first is the usual in writing, particularly when filling out a form of some sort. I hope that helps.