What ReneeM7122 mentions are two entirely different, separate 5-year rules, one for Roth conversions and one for Roth IRA distributions to be qualified distributions.
The 5-year rule for conversions must be completed before a converted amount that was taxable at conversion becomes equivalent to a regular contribution while someone is still under age 59½. Until the the 5-year conversion holding period is met or you reach age 59½, a distribution of the converted amount that was taxable at conversion is subject to a 10% recapture penalty if distributed. This is the 5-year rule that you are asking about. Each year's conversions have a separate 5-year clock which TurboTax tracks.
The entirely different 5-year rule for determining qualified distribution where earnings are distributed tax free begins on January 1 of the year for which your first Roth IRA contribution is made. Once this 5-year period has been satisfied and you have reached age 59½, earnings that are distributed are tax free. TurboTax does not track this 5-year period. TurboTax simply asks if you've had a Roth IRA before a certain year (before 2016 in 2020 TurboTax). Although that's an inaccurate way to phrase the question, that bad phrasing doesn't present a problem for most people.
