First, all Roth IRA's are treated as a single individual retirement arrangement, for all purposes including withdrawals, so opening a new account won't change any issue you might think you have.
Then, as long as you have satisfied the general 5 year clock with any Roth IRA, that clock is satisfied for all Roth IRAs.
There is a separate 5 year clock on conversions -- if you convert money now, and withdraw it in less than 5 years, you would owe a 10% penalty, but only if you are under age 59-1/2. If that is true, we can discuss how withdrawals are attributed to contributions and conversions and how the 5 year conversion clock works. But if you are over 59-1/2 or will be over 59-1/2 when you want to make a withdrawal, all your Roth IRA withdrawal will be non-taxable and free from penalties, regardless of the 5 year conversion clock.
