How many people needed for a party?

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A party must contain 5 different people with the same date of birth in 2010.

How many people must be invited to satisfy the above condition?

Is there a specific way to solve this question? I'm really lost.

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Hint: The year 2010 was not a leap year. That means it had $365$ days. The worst case scenario is having four people with each possible date of birth. If one more person attends, what happens?