Drill holes in the bottom and halfway up the sides of a 5-gallon bucket. Line with a wrung-out, wet pillowcase and place into another 5-gallon (catch) bucket.
Cut 5 gallons green apples into quarters, place in a large pot, and add enough water until you see it. Bring to a boil and then reduce heat, stirring every 3 to 5 minutes to keep from scorching.
When the apples have the texture of applesauce, pour them—seeds, skins, and all—into the pillowcase-lined bucket, cover, and let sit overnight.
The next morning, the pectin will have collected in the lower catch bucket. Don't be tempted to squeeze the remaining apples; this will cause the pectin to get cloudy. Add 1 teaspoon lemon juice to keep the pectin from browning (optional).
After the pectin has cooled, test its gelability. In a small bowl, slightly mix 1 teaspoon pectin with 2 teaspoons rubbing alcohol. Let sit for a couple of minutes. If the mass sticks close to the fork, the pectin will be great for jam. If a glob drips more than an inch from the fork, use the pectin for syrup.