It sounds like what you did over the last 5 years was done informally, without a written agreement or court order. According to the IRS Code, the parent with more than 50% custodial time files as Head of Household and claims the children as dependents. The parties are entitled to come to a different agreement, including alternating years as you both did before. At this point, however, it doesn't sound like there is an agreement, and therefore the IRS Code controls.
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