Probability with replacement of exactly (and at least) m repeats in n events of even probability k?

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What is the probability with replacement of seeing exactly m repeats in n events of even probability k?

E.g., Assume birthdays are evenly distributed across 365 days, what is the probability that exactly 5 people will share a birthday among 100 randomly selected persons with birthdays?

Next, what is the probability with replacement of seeing at least m repeats in n events of even probability k?

E.g., Assume birthdays are evenly distributed across 365 days, what is the probability that at least 5 people (5 or more) will share a birthday among 100 randomly selected persons with birthdays?

Thanks.