So meters overall have good calibration for as long as the internal shunt doesn't overheats. Thanks for answering.

The room was cold and after heating it a little bit I noticed the readings had already changed, from 4.985 A to 5.005 A with less than a ≈3°C increase in temperature, if I'm not mistaken. Unexpected, honestly speaking, in something which theoretically should be using a manganin current resistor.

If required, buying a current shunt will make current measurements a lot easier, doesn't it? With a 10 µV resolution, the meter should do fine in this regard.