C5 Corvettes from 97 thru 04 use the OBD11 system.
Unlike the earlier C4 which used the OBD1 system that can be accessed via plug located under the dash with a code scanner, or by configuring jumpers in the plug, the codes could be read out using the flashing MIL light in the instrument panel.
The C5 on the other hand can be accessed without a Scan tool, no need for fidley jumpers and plugs and things.
Utilising dash switches, in the correct sequence, the dash display will read out in plain english all codes, both current and history.
Historic codes can be reset, however, current codes will be displayed until repaired, at such time they become history and can then be reset.
If you get codes displayed, before you race off to the mechanic, google up "obd11 codes corvettes" for a helpfull youtube.
Regards.