So if I put $5500 in my Roth IRA in February, can I contribute another $5500 in May since it will be a new tax year?
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Yes, as long as those contributions are for different tax years.
Here’s an example: Assuming your IRA was established by December 31, 2015, you have until the tax filing deadline April 15, 2016 to make your 2015 contribution. You could make the 2016 contribution the following day or wait until later in the year.