First, fill the 5 kg barrel with water, and then pour the water from the 5 kg barrel into the 4 kg to 4 kg barrel, which is just full. At this point, the remaining water in the bucket with no criminal record is 1 kg.

Then pour out the water in the 4 kg bucket, and pour one kg of water in the 5 kg bucket into the 4 kg water. At this time, there is one kilogram of water in 4 kilograms of water, and there is no water in 5 kilograms of barrel.

Fill this barrel with five kilograms.

Two buckets of water add up to 6 kilograms.