According to this page, the DynamoDB is always free for 25 RCU and 25 WCU with 25GB of storage.
However, in the capacity tab of a table, it shows me an estimate cost for 10 RCU and 10 WCU to be $5.81 / month.
Will I be charged or not charged for this amount?
The estimation that you see within the DynamoDB page is not directly related to the billing calculation, therefore it will not take free tier into account. It is a simple calculator that calculates the AWS charge based on the configuration that you provided for DynamoDB.
Free tier calculations and deductions are applied at time of billing, as long as you are equal to or less than the usage for a free tier service you will not be billed for it. If you exceed this you will either be fully charged (in the case of EC2) or will pay the difference (as is the case in DynamoDB).
In DynamoDBs case this an accumulative deduction across all regions and tables, and if your account if part of an organization across all billed accounts under the organization.
