Bring apples and water to boil in heavy large saucepan. Reduce heat, cover and simmer until apples are falling apart, stirring occasionally, about 30 minutes. Cool 30 minutes.
Press apple mixture through a fine strainer into heavy large suacepan. Puree green peppers and chilies with 2 cups sugar in processor. Add to apples. Mix in remaining 3 cups sugar and vinegar. Boil over medium heat 10 minutes to blend flavors. Add pectin and boil exactly 2 minutes. Stir in red pepper. Pour into sterilized jars and seal. Shake jars occasionall as jelly cools to distribute peppers evenly. Store in cool dry place.