GT-1000CORE: Does the tuner also work for a 5-string bass?

Yes. If the "BS MODE (BASS MODE)" is set to "ON" for the selected patch during tuning, you will be able to tune the fifth string and higher.
*With the settings for the guitar (factory default), the 5th string is not detected.

Perform the steps below:

1. Press the [EFFECT] button.
   -The edit screen (effect chain) appears.
2. Turn knob [SELECT] to select “MST.”
3. Use the PAGE [<] [>] buttons to move to the last page.
4. Turn knob [2] (BS MODE) to select “ON.”
   *To save the changes, press the [WRITE] button to perform a PATCH WRITE.