Running two separate packs for drive and weapon is a common approach, but usually for larger voltage differences. Running a 5s for drive and 6s for weapon seems a little pointless (5s fully charged is 21V). Running on a single 6s pack would be more logical and just put dual rates on if you want to limit the voltage on the drive motors.

If you do go with the 2-pack route, 4000mAh is overkill for a drive pack. 1600-2000mAh would be a better size and still leave you enough in reserve. The weight saved could then go into your weapon pack (maybe take that up to 4Ah) to give you plenty of juice when running a spinner. As an example, Onyx uses a 300W scooter motor for its axe and two 550 drills for drive, and it never struggles with a 2200mAh pack for the whole robot.