Inspect five 12-ounce jars for cracks and rings for rust, discarding any defective ones. Immerse in simmering water until jam is ready. Wash new, unused lids and rings in warm soapy water.
Bring a large pot of water to a boil. Add peaches and cook until skin loosens, about 20 seconds. Drain and let cool until easily handled. Peel and pit peaches, then cut the flesh into chunks.
Return 5 cups peach chunks to the pot and mash with a potato masher. Add sugar, peach gelatin, lemon juice, and almond extract; mix well. Bring to a rolling boil, then cook for 1 minute. Remove from the heat.
Pack jam into hot, sterilized jars, filling to within 1/4 inch of the top. Run a clean knife or thin spatula around the insides of the jars to remove any air bubbles. Wipe the rims with a moist paper towel to remove any residue. Top with lids and screw rings on tightly.
Place a rack in the bottom of a large stockpot and fill halfway with water. Bring to a boil and lower jars 2 inches apart into the boiling water using a holder. Pour in more boiling water to cover jars by at least 1 inch. Bring to a rolling boil, cover, and process for 10 minutes.
Remove the jars from the stockpot and place onto a cloth-covered or wood surface, several inches apart. Let rest until cool, about 12 hours. Press the center of each lid with a finger to ensure the lid does not move up or down. Remove the rings for storage and store in a cool, dark area.