It also depends on when you send the transaction. If you send it seconds after the last block then you are probably going to have to wait ~10 mins for your first confirm. If you send ~9 minutes after that last block, then you are probably going to only wait ~1 mins for your first confirm.
Indeed, the block times follow exponential distribution.
So, after waiting for 5 minutes, the expected time to find the next block doesn't change at all.