I am an individual over 591/2 years. My Roth IRA has been in effect over 5 years. Can I withdraw earned dividends without causing any tax problems? What if the Roth has not been in effect for five years?

If Roth open 5 years and you are 59 1/2 any and all money can now be taken tax and penalty free.
If not open 5 years and you are 59 1/2 than any earnings that you withdraw are subject to taxes but no penalty.

A Roth IRA involves non-deductible contributions. All withdrawals, for tax purposes, are first, return of contributions. So, if you have contributed $2,000 a year for three years, your "cost basis" is $6,000. No income tax is assessed on the first $6,000 of withdrawals. The 5 year rule applies only to earnings, not contributions. I will be happy to provide the IRS code section, if you wish.