The 5-year clock for qualified Roth IRA distribution is associated with you, not with any particular one of your Roth IRA accounts. Since your first Roth IRA contribution was made for 2004 (or maybe even 2003), you have long since satisfied the 5-year clock, even for future Roth IRA accounts you might open and even if you had an intervening period where you had no money in Roth IRAs.
Any particular Roth IRA custodian will use code Q instead of code T for distributions after you have reached age 59½ only if you have had a Roth IRA with them for at least 5 years (and might only use code Q for particular accounts that have individually been held for 5 years). That doesn't matter, though, because you have met the 5-year requirement.
TurboTax asks if you have had a Roth IRA for 5 years. Answering Yes caused TurboTax to treat code T the same as code Q and does not report anything on Form 8606 Part III for the qualified distribution. TurboTax simply omits the qualified Roth IRA distribution from Form 1040 line 4b.
