Not sure what flexi annuity means but annuity means your monthly repayments are made up of interest and capital. So your outstanding capital amount decreases over time. Flexi may just mean you can make extra repayments off the capital amount.
I'd say your not on a tracker, but your offer letter must state something, it probably says standard variable. 5.64% is a bit on the high side, AIB's is 5.10% at the moment.
Contact your bank and they should be able to explain all.