How can I know the exact Depository Trust Company (DTC) fees on an American depositary receipts (ADR) before buying the ADR?
The DTC does not specifically charge any fees on ADRs. It is the depositary bank that charges the ADR fees you mentioned. According to the Deposit Agreement, the depositary bank is The Bank of New York Mellon (BNY Mellon), so it is BNY Mellon that charges these fees. I repeat: these fees are not DTC fees; they are fees charged by the depository bank that holds the shares underlying the ADRs.
Judging by your previous posts (1, 2), the source of your confusion is probably the Guide to the 2020 DTC Fee Schedule, which mentions:

This is only relevant for ADRs that pay no dividends where the DTC collects the fees on behalf of the depositary bank ("pass thru"). In contrast, for ADRs with dividends (such as AXAHY), the fees are collected by the depositary banks themselves by subtracting from dividends.
Indeed, the SEC's Investor Bulletin: American Depositary Receipts says:
A common practice for collection of the custody fee is for the ADR depositary bank to subtract the amount of the fee from the gross dividends paid by the bank to ADR holders. Typically, the Depository Trust Company, (DTC) will announce both the gross dividend rate and the net dividend rate after deduction of the ADR custody fee. The ADR depositary banks pay DTC the net dividend, and DTC allocates the net dividend to its users. However, a number of ADR issues do not pay periodic dividends, which prevents the fees from being collected through the above-described mechanism. In this case, DTC charges the fee to its users (i.e., banks and broker-dealers) who pass them on to their customers.
To answer the main question:
That's an upper bound (fee <= 0.05 USD/ADR). How can I know the exact fee I'll get charged?
You won't know. You only know the upper bound as stated in the Deposit Agreement. Some depositary banks do publish the historical fees, but there is no guarantee that the historical charges are indicative of future charges.
BNY Mellon happens to provide information about historical dividend payments here: https://www.adrbnymellon.com/directory/distributions-dsf. According to the historical dividend information for AXAHY, the depositary fees were:
- 2013: $0.02
- 2014: $0.02
- 2015: $0.04
- 2016: $0.04
- 2017: $0.04
- 2018: $0.04
- 2019: $0.04
- 2020: $0.04
We don't know what the fee will be in 2021. All we know is that it will be less than or equal to $0.05.