Not stupid at all!
Cycling is basically letting beneficial bacteria (BB) grow in the tank. The bb neutralize toxic ammonia and nitrite in the water. Growing enough of these bacteria can take from 2-8 weeks, but will happen anyways. To do this fast:
Get your two bettas into the divided 5 gallon, and do 2 50% water changes a week. Keep a close watch on the water parameters with this:
This will test your water. Do this every other day for the first 2 weeks. If the ammonia gets above .25 ppm do a WC. Read up more on the Nitrogen Cycle, as this was just a crash course.