Correctly Configuring and Using DAQ Device Digital TTL I/O
In my case, there is already 5V on the pin by default. So do I still need a pull-up resistor?


No. If that is TTL input pin, and it measures +5 V, then it already has a pull-up resistor to +5 V. An open-collector (or open-drain) driver is appropriate in that case.

It would be helpful to check with the user manual of the actual device which has that input, as that may (should!) give more details of how its inputs should be driven.