Your charger output is file.
6s 5A consumes about 3.7v x 6 x 5A = 111W.
When reaching 4.2V, it only consumes about 126W.
If your power supply is sufficient and your lipo pack is not damaged, then it seems your lipo pack has reached 4.2V per cell and your charger is lowering the charging current.
Are you sure this is the charger output? Because it sounds like an output rating of a power supply to me. Some chargers cannot utilze all power as they are not capable to charge the battery at this rate so they will just lower the charging current just like your situation.
For example, if you connect a 100w charger to a 350w power supply, the charging power of your system will be only around 100W