According to the schematics
for the board CrossRoads found, you should be OK.
The 5 volts are all labeled the same, which should mean they are connected.
So you do not need to connect to Arduino's 5 volt supply if you use some other supply.
But still you should be aware of something quite important.
That is about the regulator on your board (still assuming that you have that board), and the voltage you are supplying it.
You are supplying 6 volts and this needs to be converted to 5 volts, so a difference of 1 volt.
of the 78M05 tells about the dropout voltage of 2 volts on page 2.
This means that the minimum difference between input and output needs to be larger than 2 volts for the regulator to provide a stable 5 volts.
Are you able to supply 7.5 or 9 volts instead and would your motor be OK with that ?