I've opened a 80A rated energy meter and found out the CT's have a writing " 5 (80)A / 2.5mA/0.1 " , is it 5A or 80A ?

Look at the IEC620xx specs for energy meters and these CT specs will make sense. The IEC approach is to define something they call a basis current. Its not the maximum current the meter is designed for. Its frequently 1/6 of the maximum current, although it could be any fraction. You will find meters where the basis current is 1/10th, 1/12th, 1/20th and other fractions of the maximum operating current. Its just a reference point, really. No meter is going to be as accurate at small currents as it is at large currents, or as accurate at poor power factors as it is at unity power factor. The IEC specs define an error mask for each class (2%, 1% 0.5%, or 0.1% accurate) of meter that allows for this reality, and defines the maximum spread of error allowed at various fractions of the basis current, for various power factors. Above the basis current the meter needs to maintain the accuracy specified at the basis current.

The CT you are looking at has been designed to meet the requirements for a 0.1% accurate meter with a basis current of 5A and a maximum operating current of 80A. So, for this CT the maximum current can be up to 16 times the basis current, while complying with the IEC specification. At 5A the secondary current will be 2.5mA. There should also be a specification for the maximum burden resistance before the CT fails to give the specified accuracy.